Kate Osborne, who is standing in the seat of Jarrow, posted the image of the former prime minister online during the previous election.
It comes as two hopefuls to become Labour MPs have been blocked from standing because of alleged anti-Semitic comments, while others have been criticised for social media comments.
Ms Osborne has since apologised, but a group of 27 female Labour candidates is calling on the party’s general secretary Jennie Formby and the ruling National Executive Committee (NEC) not to allow her to stand when it decides her fate later on Saturday.
Among those who have signed the letter are Liz Kendall, Jess Phillips, Yvette Cooper, Lucy Powell, Cat Smith and Vicky Foxcroft.
In a letter seen by PoliticsHome the candidates urge the party to stop Ms Osborne from being able to run for the party.
The letter says: “The impact of such images are clear – they incite intimidation and violence against female politicians.
“Many of our Labour colleagues – and indeed politicians from all political parties – have been subject to similar disturbing content online.
“When women in public life are facing unacceptable levels of intimidation, sharing this image not only indicates an extreme lack of judgment, but further feeds into the cycle of abuse that we are all currently experiencing.
“If Kate Osborne is selected, it would undermine any claim our party makes to stand resolutely against the harassment and intimidation of women in public life.”
Meanwhile, shadow education secretary Angela Rayner said posting the image was “unacceptable” but said the decision on Ms Osborne’s future was up to the NEC.
Speaking to BBC Radio 4’s Today programme, Ms Rayner added: “As somebody who’s faced a level of abuse and death threats as a politician, I think a lot of people out there really don’t see the vitriol and the nastiness that’s online that’s pointed towards politicians at the moment.”
In a statement to Huffington Post about the Theresa May image, Ms Osborne said: “I shared an image on social media of a film parody poster making light of Theresa May’s forced and robotic statements about her ‘strong and stable government’ in the run-up to the 2017 general election.
“I unreservedly apologise for having shared this image.
“As a woman, I am extremely concerned about the abuse and threats that women in politics face and if elected I will work with colleagues to challenge misogyny, hate and division in politics and beyond.”