The police said the incident was "criminal rather than nationalistic". The victims were a man and a woman, Haaretz newspaper said.
Police are searching for a black-clad gunman who fled the scene after opening fire in the centre, on Nachmani street.
Witnesses said the gunman fired in all directions with a handgun.
Representatives of the gay community said they believed the attack was homophobic.
Media reports said a nightclub was attacked, but local sources told the BBC News website the shootings took place at the headquarters of the local lesbian and gay rights association.
Reports say all gay clubs and bars in the city have been closed.
Correspondents say Tel Aviv has a vibrant gay scene but some areas of Jewish society are not tolerant of homosexuality.
"It is not surprising that such a crime can be committed [because of the] incitement of hatred against the homosexual community," AFP news agency quoted gay and lesbian community leader Mai Pelem as saying.
Annual gay pride marches are often met with violent protests by ultra-Orthodox Jews in Jerusalem.
Tel Aviv has in the past been targeted in attacks by Palestinian militants.
Follow @BreakingNews on twitter for the latest. They're saying that fatalities are up to 3, most are youth, and 15 are injured.