Their absences, which was to give them a break from the game, adds to that of fast bowler Stephen Harmison who asked not to be considered for Zimbabwe on moral grounds to protest the policies of President Robert Mugabe.
Ashley Giles was also given the option of being rested, but has chosen to make himself available and has been included in the 14-man squad.
The missing senior players means that four players uncapped at One-Day International level have been included - Ian Bell, Kevin Pietersen, Matthew Prior and Simon Jones.
Flintoff, Giles, Harmison and Trescothick have all been included in a 15-man one-day squad to tour South Africa in the New Year together with Ian Bell and the Worcestershire pace bowler Kabir Ali.
The England Cricket Board (ECB) Chairman, David Morgan, said on Tuesday: "Following conversations I had with Michael Vaughan and Duncan Fletcher on Sunday, the ECB Management Board yesterday accepted a recommendation from the selectors that three senior players should be rested from the tour to Zimbabwe on cricketing grounds.
"Andrew Flintoff and Marcus Trescothick both subsequently accepted the invitation to be rested while Ashley Giles declined.
"The option of resting Michael Vaughan was discussed by the Management Board which is well aware of the workload he has faced in recent months and hugely appreciative of his efforts in leading the team to seven consecutive Test wins and to the ICC Champions Trophy Final," he said.
"The ECB and the team have, however, faced up to the situation in the knowledge that the tour to Zimbabwe must go ahead subject to it being safe and secure to proceed and in the absence of firm instruction from government to the contrary."
"After carefully considering the matter, Michael has chosen to lead the team in Zimbabwe mindful of his responsibilities both to his fellow players and to the long-term future of cricket in this country. He deserves great credit for doing so," he stated.
"Neither the ECB nor the captain condones the situation in Zimbabwe and I would like to re-emphasize that the team will not be involved in state functions during this tour."
Vaughan said that he would have welcomed an extended break from the game after a busy season, but facing what he said was an "extraordinary" situation in touring Zimbabwe, felt that he had a duty as captain to go along.
The ECB also confirmed that England will play two warm-up matches against Namibia during an eight-day stay in the country prior to the tour of Zimbabwe.
England One-Day Squad to tour Zimbabwe: Michael Vaughan (Yorkshire, capt), James Anderson (Lancashire), Gareth Batty (Worcestershire), Ian Bell (Warwickshire), Paul Collingwood (Durham), Ashley Giles (Warwickshire), Darren Gough (Essex), Geraint Jones (Kent), Simon Jones (Glamorgan), Kevin Pietersen (Nottinghamshire), Matthew Prior (Sussex), Vikram Solanki (Worcestershire), Andrew Strauss ( Middlesex), Alex Wharf (Glamorgan)
England One-Day Squad to tour South Africa: Michael Vaughan (Yorkshire, capt), Kabir Ali (Worcestershire), James Anderson (Lancashire), Gareth Batty (Worcestershire), Ian Bell (Warwickshire), Paul Collingwood (Durham), Andrew Flintoff (Lancashire), Ashley Giles (Warwickshire), Darren Gough (Essex), Stephen Harmison (Durham), Geraint Jones (Kent), Vikram Solanki (Worcestershire), Andrew Strauss (Middlesex), Marcus Trescothick (Somerset), Alex Wharf (Glamorgan).