Former prime minister Sir John said it would be "utterly and totally unacceptable" for any British premier to shut down Parliament, and he would seek a judicial review if it happened.
Mr Johnson has refused to rule out proroguing Parliament to prevent MPs blocking a no-deal exit from the European Union on October 31.
Sir John told BBC Radio 4's Today: "You cannot and should not bypass Parliament in this fashion. I cannot imagine how anyone could conceivably think that is right."
In order to prorogue Parliament, shutting it down until the next state opening, a prime minister would have to ask the Queen to formally allow it.
Although the Queen's decision could not be challenged, Sir John said the advice of the prime minister could be.
The monarch would be "in the midst of a constitutional controversy that no serious politician should put the Queen in the middle of", Sir John said.
"I for one would be prepared to go and seek judicial review to prevent Parliament being bypassed," he added.
The potential suspension of Parliament was one of the issues on which Mr Johnson and his rival Jeremy Hunt clashed in a televised showdown on Tuesday night.
Mr Hunt issued a stark warning about the prospect of suspending Parliament.
"When that has happened in the past, when Parliament has been shut down against its will, we actually had a civil war," Mr Hunt said.
But Mr Johnson said: "I'm not going to take anything off the table, any more than I'm going to take no-deal off the table.
"I think it's absolutely bizarre at this stage in the negotiations for the UK - yet again - to be weakening its own position."
Sir John, who is backing Mr Hunt for the leadership, said: "There is no conceivable justification, wherever we are, in closing down Parliament to bypass its sovereignty.
"I seem to recall that the Brexiteers, led by Mr Johnson, actually campaigned in the referendum for the sovereignty of Parliament... They can't be concerned for the sovereignty of Parliament except when it is inconvenient to Mr Johnson."