The Grand Hyatt, the Radisson SAS and the Days Inn Hotel were all hit in what appeared to be a coordinated attack.
The explosions were caused by three suicide bombers, Jordan's official news agency, Petra, reported.
Deputy Prime Minister Marwan Muasher g said there was no claim of responsibility, but Abu Musab al-Zarqawi, the Jordanian-born leader of al-Qaida in Iraq, was a "prime suspect."
AP reporter Jamal Halaby, who was at the luxury Grand Hyatt popular with diplomats and tourists, counted seven bodies being taken away and many more wounded being carried out on stretchers.
Reports from the Radisson suggested that a bomb exploded through the ceiling of a banquet hall where a wedding was taking place.
The hotel is popular with American and Israeli tourists and was the target of a plot in 2000.
In the past two years, Amman has become a base for Westerners doing business in Iraq, the AP reported. The hotels are also a gathering spot for affluent Iraqis who have fled their country's violence.
In July, prosecutors indicted five Jordanians in an alleged plot to attack intelligence agents, tourists and hotels in Amman. The following month, al-Qaida in Iraq claimed responsibility for a rocket attack that barely missed U.S. warships docked in the Jordanian port of Aqaba.