Sir Tim drew criticism after saying the "trouble with girls" in labs was they "cry" when criticised and "fall in love" with male counterparts.
Prof Cox called the remarks "ill-advised" but said it was "wrong" that he had had to leave his University College London and Royal Society posts.
Sir Tim apologised for causing offence.
The 72-year-old left his positions after his comments - which were branded "sexist" by some - prompted a furious online backlash.
He told the Observer he had been "hung out to dry".
Speaking to BBC Radio 4's World at One programme, Prof Cox said the situation was "serious", but he questioned whether Sir Tim should have resigned.
"Is it appropriate to hound someone out of their position at a university or indeed, is it appropriate for the university to react in the way that UCL in this case did and ask someone to resign or else threaten to sack them?" Prof Cox said.
"We do have a problem about these mobs - you call them Twitter mobs, descending on people who use language ill-advisedly and cause great professional ruin. I don't think that is the case although he felt that.
"To have a Nobel prize winner and by all accounts a great scientist and a good person being hounded out of a position at UCL, after all those years of good work in science, I think that's wrong and disproportionate."
Sir Tim, who was awarded the Nobel prize in 2001 for his work on how cells divide, reportedly told a conference in South Korea: "Let me tell you about my trouble with girls.
"Three things happen when they are in the lab: you fall in love with them, they fall in love with you, and when you criticise them they cry."
He later told the BBC he stood by some of the comments, and said: "I did mean the part about having trouble with girls," But he added he was "really sorry" if he had caused offence.
Nobel laureate Sir Tim Hunt should not have been "hounded" into resigning over his remarks about women in science, Prof Brian Cox has said.