After the incident, near a military headquarters, huge blasts were heard in Gaza – an apparent Israeli strike on the football stadium.
Eleven people were killed in Gaza on Wednesday, the health ministry said.
Efforts to broker a truce between the Hamas movement and Israel continue.
After eight days of exchanges of fire between Israel and Palestinian militants in Gaza, US Secretary of State Hillary Clinton is now in Cairo for talks with the Egyptian president.
Earlier, Hillary Clinton and UN Secretary General Ban Ki-moon held talks in the West Bank with the Palestinian Authority President Mahmoud Abbas.
Militants in Gaza have been firing more rockets at Israel.
Israeli Prime Minister Benjamin Netanyahu’s spokesman Ofir Gendelman said on his Twitter account that the explosion was caused by a bomb and that it was a “terrorist attack”.
Of the 21 injured, three were suffering from moderate to light injuries – including shrapnel wounds and burns – and were undergoing surgery, a spokesman for the Ichilov medical centre in Tel Aviv said.
Six had already been released and the rest were suffering from anxiety, he said.
The bus was reportedly passing the military headquarters in the city at the time of the blast.
Police believe a bomb was planted on the bus and they are still searching for a suspect.
Hamas, the Islamist movement which has governed Gaza since 2007, has praised the attack but has not said it was behind the blast.
Celebratory gunfire reportedly rang out in Gaza when local radio relayed news of the attack.
A series of massive explosions in Gaza, in an apparent Israeli strike on the sports stadium have been reported. Reports from Gaza say the stadium has in the past been used a site to launch rockets.
According to Israel’s ministry of foreign affairs, the last bomb attack in Tel Aviv was in April 2006, when a suicide bombing on a restaurant killed 11.
The bus blast comes on the eighth day of the current flare-up in violence between Israel and militants in Gaza.
Some 147 Palestinians and five Israelis have been killed.
Other sites hit in Gaza included a banker’s villa, tunnels to Egypt used by smugglers and a media office, said to be linked to Hamas, that was situated two floors above the Agence France-Presse office in Gaza City.
The IDF said 62 rockets fired by militants from Gaza had hit Israel so far on Wednesday, while another 20 were intercepted by its Iron Dome missile defence system.
The latest violence will further complicate ceasefire discussions taking place in the region.
The two international mediators are both expected to hold talks with Egyptian President Mohammed Mursi in Cairo.
In the West Bank, Ban Ki-moon expressed “profound concern” at the civilian casualties in Gaza and also called on militants to end immediately their “indiscriminate attacks on Israeli population centres”.
Hillary Clinton held talks with Israeli PM Benjamin Netanyahu in Jerusalem before heading to Cairo.
Officials from Hamas had suggested on Tuesday that a truce would come into effect at midnight, but Israel later said it had not agreed to a text.
Israel’s demands include no hostile fire of any kind from Gaza and international efforts to prevent Hamas from re-arming, while Hamas is demanding an end to the blockade on Gaza and targeted killings by Israel.
Israel launched its current offensive a week ago with the killing of Hamas military leader Ahmed Jabari. The Israeli government says his assassination, and the subsequent offensive, is designed to end rocket fire from Gaza.
Israel has troops massed along the Gaza border but says it is holding off on a possible ground invasion as talks continue.
Ceasefire demands
Israel
Hamas
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