The Education Secretary shouted "disgrace, you're a disgrace" at Tory and Liberal Democrat rebels, according to the SNP's Angus Robertson and lobby journalists watching from the press gallery.
Robertson, the SNP's Westminster leader, told Sky News he watched on as Gove had to be "persuaded to calm down" following the outburst.
He said "emotions were running high", adding: "This is an unprecedented defeat for the Conservative-Lib Dem coalition, for the Prime Minister David Cameron and for Nick Clegg, so obviously there were senior figures in the Government who were very upset that a number of their colleagues voted against the Government and abstained.
"I watched the English Education Secretary Michael Gove shout, 'A disgrace, you're a disgrace' at a number of Conservative and Lib Dem rebels.
"He had to be persuaded to calm down by a number of his colleagues.
"I retorted, 'It's called democracy', because that was what happened. We have finally learned the lessons from Iraq."
Former Lib Dem leader Sir Menzies Campbell suggested the US Congress would be less sympathetic to upholding aspects of the "special relationship" such as intelligence sharing, missile sharing and free trade in the light of last night's vote.
He told BBC News: "If you're a congressman in the United States asked to be sympathetic towards these things, in the light of tonight's decision what do you think your reaction would be?"
Asked about Cameron's position, Campbell said: "It's loyal to say things will go on as ever. The truth is they have been damaged. But the truth is some of the damage was done by very many of the same people that voted against them tonight earlier this year when it came to the question of the European Union."
Defence Secretary Philip Hammond told BBC's Newsnight that Cameron was "disappointed" by the vote but was clear that "the mood of Parliament is that Britain should not be involved in military action and Britain will not be involved in military action".
He said: "We are now clear that we are not now going to be part of any military action - that probably means we will not be part of any planning or discussion.
"It is certainly going to put a strain on the special relationship."
Suggested For You
SUBSCRIBE AND FOLLOW
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements.Learn more