Scottish Tory leader Douglas Ross previously said Mr Johnson's position was "no longer tenable" amid the row over Downing Street parties during lockdown.
However, he later withdrew this, arguing the war in Ukraine had changed the situation.
Last week the Metropolitan Police said 20 fines had been issued in relation to partygate and more could follow.
Downing Street confirmed the Prime Minister had not received a fixed penalty notice so far.
Appearing on the BBC's Sunday Show, Mr Simpson, his party's transport spokesman in Holyrood, was asked if Mr Johnson should stay in office if he is fined.
He said: "Well, the Prime Minister hasn't been fined, so it's completely speculative to say that, so I'm not going to sit here and say what should happen."
Mr Simpson added: "I think right now, when we've got the situation in Ukraine, it's completely the wrong time for anyone to be calling for the Prime Minister to go.
"The message that would send out to Vladimir Putin would be completely wrong.
"We need to be concentrating on helping the people of Ukraine and not calling for prime ministers to go. It's the wrong time."
Scottish Labour leader Anas Sarwar said: "Boris Johnson is a liar, he's incompetent, he's corrupt and the sooner he loses office the better it is for the United Kingdom."
It came as UK Labour's shadow business secretary Jonathan Reynolds said everyone issued with a fine over lockdown parties in Downing Street should be identified, including the Prime Minister’s wife Carrie Johnson.
When asked specifically whether Mrs Johnson should be named if she has been fined, Mr Reynolds told the BBC: “Yes, I think anyone who’s been in Downing Street should be named if they have been part of this.
“I think all people want is some transparency as to what really went on in Downing Street.”
He added: “All people want to know is, has the Prime Minister been truthful and has Downing Street as an institution been following the same rules as everyone else?”