The policemen had been inspecting the rudimentary bomb after the train, in the Menufiya province north of Cairo, stopped at a station when the explosive went off, the officials said.
The bomb exploded as police evacuated passengers from the carriage, also wounding eight people, state television reported.
Dozen of policemen and soldiers have been killed in militant attacks since the army overthrew Islamist president Mohamed Morsi last year and launched a bloody crackdown on his supporters.
Most of the deadliest attacks have taken place in the Sinai peninsula, where militants based there killed at least 30 soldiers in one attack last month.
But the militants have also expanded in the capital and the Nile Delta, targeting police stations and checkpoints in near monthly attacks.
A bomb outside Cairo University on October 22 wounded nine people, including a police general.
Ajnad Misr, a militant group that has killed several policemen in Cairo bombings, claimed that attack, saying in a statement it was in response to repression of student protesters.
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The explosion occurred near the site of a bombing in April that killed a police general, and where riot policemen are stationed on foot and in armoured vehicles to confront frequent protests by pro-Islamist students.
The group also claimed responsibility for bombing a checkpoint outside the foreign ministry in September that killed two policeman.
It says the attacks are revenge for the deaths of hundreds of pro-Morsi protesters in clashes with police after his overthrow in July 2013.
At least 15,000 Islamists have been arrested on suspicion of protesting or participating in violence since Morsi's overthrow.
The authorities have blamed Morsi's now blacklisted Muslim Brotherhood for the violence, although the group insists it is committed to peaceful protests.
President Abdel Fattah al-Sisi, the army chief who overthrew Morsi and was subsequently elected, has vowed to eradicate the Islamist movement, which continues to hold small protests.
The deadliest bombings have been carried out by a resilient militant group based in Sinai, Ansar Beit al-Maqdis.
The group is believed to be responsible for last month's attack on an army checkpoint that killed at least 30 soldiers, the deadliest in years.
Sisi declared a state of emergency law in parts of northern Sinai after that attack and the military has begun demolishing homes along the Sinai border with Gaza to create a buffer zone.