Michael was not available for an interview Monday, but spokeswoman Jean Graham says the letter was sent to Michael in an email over the weekend, just after the party leader returned from vacation.
Graham says the letter asks for a leadership convention in 2014 to ensure party renewal ahead of a provincial election in 2015.
She says for a convention to be held, Michael would have to resign as leader or the party executive would need to sign a petition.
Graham says all four NDP caucus members — Dale Kirby, Gerry Rogers, George Murphy and Christopher Mitchelmore — signed the letter.
She says Michael has already met with a couple of the caucus members and plans to meet with the others to discuss their concerns.
Graham says Michael was surprised by the letter as she was not aware of any issues prior to receiving it.
The four caucus members could not be reached for comment.