Lampard, who has a knee injury, and Bertrand, sidelined by a throat infection, missed Friday's 5-0 victory over San Marino, but England manager Roy Hodgson was hopeful they would recover in time for the Poland clash.
But, after reporting to England's training camp on Sunday to be assessed by the medical team, it was decided that neither would be able to take part.
"Lampard (calf) and Bertrand (illness) did not take part in England's 5-0 win over San Marino, and will not be ready for Tuesday's game. Roy Hodgson and his squad of 23 players travel to Warsaw on Monday morning."
Lampard and Bertrand were sidelined less than 24 hours after it was confirmed Theo Walcott was ruled out of the Warsaw showdown after sustaining a chest injury in a heavy challenge with San Marino's goalkeeper, Aldo Simoncini.
Lampard's absence is slightly offset by the return from suspension of captain Steven Gerrard, who is likely to form a three-man midfield with Michael Carrick and Tom Cleverley against Poland.