The Prime Minister survived a confidence vote by 211 to 148 – with the Scottish Conservative leader amongst those voting for a change of leadership.
But calls for Mr Johnson to quit remain following two by-election defeats in Wakefield, West Yorkshire, and Tiverton and Honiton in Devon.
Tory MP Andrew Bridgen has outlined plans to stand for the 1922 Committee’s executive role later this week on a manifesto pledge to change the rules which would allow a second vote of confidence to be held.
Current rules state that confidence votes can only be held once a year.
But while Mr Ross is in favour of leadership change, he has said it would be “wrong” to change the rules.
Speaking on BBC’s Sunday Show, he said: “I’m a member of the 1922 Committee but I’m not on the executive committee and it is for the executive committee to look at rule changes.
“And clearly there is an election, I think, next week or the week after, and some candidates, their pitch is that they would change the rules.
“I personally don’t think we should change the rules midway through a process. I think that’s the wrong way to do it.
“But we saw with Theresa May, she lost a vote of the 1922 Committee and it didn’t take a rule change.
“She looked at the situation a few months on and she stepped down herself.”
But the Prime Minister has said he has no plans to resign.
Instead, he has said he is pushing to stay in power until around the mid-2030s.
Speaking in Kigali, Rwanda, Mr Johnson said: “At the moment I’m thinking actively about a third term and what could happen then, but I will review that when I get to it.”
Asked whether his party will lose the next general election if Mr Johnson remains leader, Mr Ross said he “was not looking at that”.
“We’ve got probably two or more years to go until the next general election,” he said.
“And the biggest issue for me is the priorities that the government, both here in Scotland and across the UK, should be focusing on which is the cost-of-living crisis and all of the issues that are facing our NHS, education, justice and local government.”