Douglas Ross said he shared the fury of the public over the “unacceptable” actions of the prime minister.
But he said it would be wrong to destabilise the UK government while the war in Ukraine was ongoing.
Chancellor Rishi Sunak and the PM’s wife, Carrie Johnson, will also be fined over parties in Downing Street.
Downing Street has confirmed Mr Johnson’s fine was in relation to an event he attended on 19 June 2020 to celebrate his birthday.
His wife and Mr Sunak were also reported to have been at the gathering, with an ITV report saying the prime minister had been presented with a cake while people sang Happy Birthday to him.
The fines are among more than 50 to have been handed out so far by officers from the Met, who have been investigating alleged Covid law-breaking at 12 gatherings in Whitehall and Downing Street during lockdowns in 2020 and 2021.
Mr Johnson is the first serving prime minister of the UK to be sanctioned for breaking the law.
Scotland’s first minister, Nicola Sturgeon, and Labour leader Sir Keir Starmer have both called for Mr Johnson and Mr Sunak to resign.
But Mr Ross said in a statement that removing the prime minister would “destabilise the UK government when we need to be united in the face of Russian aggression and the murdering of innocent Ukrainians.”
He said the public was “rightly furious” at what had happened in Downing Street during lockdown, adding: “I understand why they are angry and share their fury.
“The behaviour was unacceptable. The prime minister now needs to respond to these fines being issued.
“However, as I’ve made very clear, in the middle of war in Europe, when Vladimir Putin is committing war crimes and the UK is Ukraine’s biggest ally, as President Zelensky said at the weekend, it wouldn’t be right to remove the prime minister at this time.”
Awkward doesn’t really cover the spot that Douglas Ross finds himself in. His credibility is in question.
Having concluded the prime minister’s position was “untenable” in January, before the police investigated – he’s now arguing the opposite when Boris Johnson has been fined.
This about turn is not new. He made that the early stages of the Ukraine war, on the basis that the UK should present a united front against Russia.
Partygate has certainly united the opposition in demanding the PM’s resignation, with some arguing the UK cannot afford to be represented by a lawbreaking leader on the world stage.
There’s division within the Conservative party too, with former Scottish leader Ruth Davidson sticking to her view that Mr Johnson has lost the “moral authority” to govern. Awkward indeed.
Mr Johnson has confirmed that he has paid the fine, and he apologised but insisted he would not resign over the matter.
“I accept in all sincerity that people had the right to expect better,” he said in an interview, at his Chequers country retreat.
“[But] now I feel an even greater sense of obligation to deliver on the priorities of the British people.”
Reports that parties had been held in Downing Street during lockdown first emerged in December of last year, with Mr Johnson initially insisting that “the guidelines were followed at all times”.
He later apologised for attending a drinks party in the Downing Street garden, but told Parliament he believed he had been attending a work event.
This admission initially resulted in Mr Ross saying the prime minister’s position was no longer tenable, and he wrote to the 1922 Committee of backbench Tory MPs in January calling for a leadership contest.
But he withdrew the letter in March, arguing that calls for Mr Johnson to quit should be put on hold following the Russian invasion of Ukraine.
Mr Johnson subsequently attended the Scottish Conservative conference in Aberdeen, where he was welcomed onto the stage by Mr Ross.
Mr Sunak was also asked in the Commons in December if he attended Christmas parties said to have taken place in 2020, and replied: “No, I did not attend any parties.”
What has the reaction been?
First Minister Nicola Sturgeon tweeted that Mr Johnson had broken the law and “repeatedly lied to parliament about it”, and must therefore resign.
She added: “The basic values of integrity and decency – essential to the proper working of any parliamentary democracy – demand that he go.
“And he should take his out of touch chancellor with him”.
Labour leader Sir Keir said the fines showed that the Conservatives were “totally unfit to govern”, adding: “Britain deserves better.
“Boris Johnson and Rishi Sunak have broken the law and repeatedly lied to the British public. They must both resign.”
Scottish Green MSP Gillian Mackay said Mr Johnson and Mr Sunak were “a disgrace” and that “if they have a shred of dignity left they will resign immediately.”
And Scottish Liberal Democrat leader Alex Cole-Hamilton said parliament should be recalled for a vote of no confidence in the prime minister.
Campaigners from the Covid-19 Bereaved Families for Justice group also said there was “simply no way either the prime minister or chancellor can continue”.
Scottish Secretary Alister Jack issued a statement in support of the Mr Johnston, saying he remained the “right person to lead this country at such a crucial time.
Former Scottish Conservative leader Ruth Davidson, however, tweeted that he had lost moral authority and he “should go”.