The blast at the Sunubar Hotel sent frightened guests of the three-storey hotel running into the street, some barefooted, others with bloodstains on their clothes.
Dr Hassan al-Juburi, director of the Tikrit Teaching Hospital, said the blast happened at about 8pm Iraq time.
The eight injured included two policemen and all the victims were Iraqis, officials said.
US military officials blamed the attack on “anti-Iraqi forces”, the term they use for insurgents.
Tikrit residents reached by telephone said the hotel housed mostly construction workers who had no connections with the American military.
Tikrit, about 130km north of Baghdad, is the hometown of former leader Saddam Hussein and was one of the centres of the Sunni Muslim insurgency.
However, the city has become relatively quiet in recent months.
US and Iraqi officials said a second rocket was fired at a US military position but caused no damage or casualties.
The attack came just hours after Iraq’s interim president, Iyad Allawi, pledged to restore order in the country ahead of national elections promised by January.
Mr Allawai said he was ready to use force, if necessary, with the support of US-led forces.
Iraq is on the brink of an all-out assault on rebel-held Fallujah as deadly clashes erupted between US troops and insurgents in the neighbouring city of Ramadi.
“We have entered the final phase to solve the Fallujah problem,” said Mr Allawi.
“If we cannot solve it peacefully, I have no choice but to take military action. I will do so with a heavy heart,” he told a news conference in Baghdad.
Mr Allawi said he has held talks with religious and tribal leaders from the Sunni Muslim insurgency bastions of Fallujah and Ramadi, west of Baghdad, and the northern city of Mosul.
He said they all wanted the government to assert its authority in these hotspots.
The prime minister laid out three conditions that would spare Fallujah and other rebel cities military action.
These include the exit of foreign fighters and insurgents, the handover of heavy and medium-sized weapons and allowing the government to begin the process of reconstruction in these cities.
In a sign of progress, the prime minister announced that 167 foreign fighters, including Syrians and Sudanese, had been arrested in Iraq.
Mr Allawi also confirmed the killing of four leaders in the militant group of Abu Musab al-Zarqawi, the alleged frontman for the Al-Qaeda terror network in Iraq.