Abu Teir, who was the number two candidate on the Hamas list in January's parliamentary election, was detained for several hours after police issued a prohibition order against a planned rally by the Islamist movement in the city's Zur Bakher neighbourhood.
A Jerusalem district police spokesman said the "seven men are suspected of pursuing preparations for an illegal rally and were taken for questioning".
Police released the seven Hamas members on bail several hours later, the spokesman said.
The MP comes from Zur Bakher.
Israel bans all Palestinian political activity in East Jerusalem, which was occupied and then annexed after the 1967 Middle East war.
The Palestinians want to establish the capital of their promised future state in East Jerusalem.
The Hamas-led government's Jerusalem affairs minister, Khaled Abu Arafeh, was arrested on April 6 but was later released without charge.