Turkey's news agency said embassy security guards captured the attacker. The report quoted anonymous officials from the embassy.
A newspaper identified the attacker as a Palestinian who tried to seek asylum at another embassy four years earlier.
"This is a hostage situation," Israeli Foreign Ministry spokesman Yigal Palmor told The Associated Press.
A lawyer told Israel Radio that the hostages, the consul and his wife, escaped.
Israel Radio reported from the scene that rescue workers with stretchers tried to enter the seaside embassy compound but left without bringing out any wounded.
The radio report said Turkish officials were not allowing Israeli police or rescue workers to enter the embassy.
"We know of one lightly injured person," Eli Binn of the Israeli rescue service told Channel 10 TV.
The Israeli Maariv newspaper said the man called the paper, identifying himself as Nadim Injaz, a Palestinian who sought asylum at the British Embassy in Tel Aviv in 2006. He said he had a flammable liquid and threatened, "I will kill any Jew that enters."
The Turkish Anatolia news agency reported that security guards at the embassy captured the attacker, and the situation was under control.
Lawyer Shafik Abuani told Israel Radio that he talked to the man three times by telephone, trying to calm him down. The lawyer said Injaz threatened to burn the embassy down if he is not granted asylum.
It was unclear what his relation to the hostage-taker was.
Abuani said Injaz demanded to be flown to Turkey and said he was being persecuted by the Israeli Shin-Bet security force.
The lawyer said only the Turkish consul and his wife were in the building at the time, and they escaped. "I am in touch with the consul all the time by cell phone, and nothing happened to them, they're OK," he said.
Turkey withdrew its ambassador from Tel Aviv in the wake of the Israeli attack on a Turkish flotilla heading for Gaza on May 31, when nine pro-Palestinian activists were killed.
Associated Press Writer Ceren Kumova in Ankara contributed to this report.