Another policeman was wounded in the attack, which struck at around 9:15 pm (1815 GMT) in the city, hometown of now executed dictator Saddam Hussein, Salaheddin provincial police said in a statement issued to journalists.
A doctor at Tikrit's main hospital confirmed that two policemen were killed and one was wounded.
Although no group claimed responsibility for the attack in its immediate aftermath, al-Qaeda's offshoot in Iraq has vowed to carry out revenge attacks after the May 2 killing of its leader Osama bin Laden in a US raid in Pakistan.
Tuesday's attack came little more than a month after a March 29 al-Qaeda raid on the city's provincial council offices, that led to an hours-long gun battle with security forces which left 58 people dead.
Tikrit remains volatile. In mid-January, a suicide bomber killed 50 people in a crowd waiting outside a police recruitment centre, in the first major strike in Iraq since the formation of a new government on December 21.