One of the policemen was said to be in a serious condition.
The clashes with gunmen broke out on Saturday in Dair al-Balah when police tried to make an arrest. The reason for arresting the man was not divulged.
Persistent security chaos in the Gaza Strip has been exacerbated since Israel withdrew all troops and settlers from the Palestinian territory in September after a 38-year occupation.
In the West Bank, meanwhile, clashes flared briefly between Palestinian resistance fighters and Israeli soldiers after troops moved into the northern city of Jenin.
Israeli troops later left the area without making any arrests.
The army said it had fired artillery into a self-declared "no-go zone" in the northern Gaza Strip from where Palestinian fighters have been firing missiles into southern Israel.
Observers ordered out
Also on Saturday, followers of the Al-Aqsa Martyrs' Brigades ordered international observers overseeing this month's Palestinian election to leave the Jenin area of the northern West Bank.
"We are sorry to tell you that you must leave Jenin as soon as possible," said a statement from the Jenin branch of the Brigades received by AFP.
"We ask you to understand that this step is not against you. It is against the occupation and against the international community which has done nothing to stop the Israeli army's escalations against our people."
The Al-Aqsa Brigades, a group of largely autonomous cells nominally loyal to the ruling Fatah movement, had previously threatened to kidnap monitors in the Gaza Strip unless a series of demands were met, including guarantees that elections take place in east Jerusalem on 25 January.