Israel had sought to strip Abu Teir, Khaled Abu Arafeh, a former minister for Jerusalem affairs, and Ahmad Atoun and Mohammed Totah, both MPs, of their Israeli-issued identity cards.
The men have appealed the decision and Abu Teir was due to appear in court on Thursday.
Atoun said he was driving with Abu Teir in the Sur Baher neighbourhood, where the latter lives, when they were pulled over by police asking to see their IDs.
“We told them we do not have IDs. They arrested Muhammad Abu-Teir and told me I have two days remaining to stay in Jerusalem,” he told the Reuters news agency.
Many Palestinians fear their expulsion could set a precedent for the removal of more of the nearly 270,000 Palestinians living in east Jerusalem, which Israel occupied in 1967 in a move not recognised internationally.
Palestinians living in east Jerusalem hold Israeli-issued IDs that allow them to travel freely in Israel and the West Bank, collect government benefits and vote in local but not national elections.
The Palestinians want east Jerusalem to be the capital of their future state, while Israel views the entire city as its “eternal, indivisible” capital.
Richard Falk, the UN special rapporteur on human rights in the Palestinian territories, cited the four men’s case in a statement on Tuesday saying that he saw it as part of “a larger, extremely worrying pattern of Israeli efforts to to drive Palestinians out of East Jerusalem – all of which are illegal under international law”.
Israel has said they are being expelled because they are members of Hamas, which Israel, the United States and the European Union consider a “terrorist” organisation, although it won Palestinian legislative elections in 2006.
Abu Teir was among dozens of Hamas politicians from Jerusalem and the West Bank that Israel rounded up after the polls. He was freed in May, but was then told his Israeli-issued ID was being revoked.