A police lieutenant from the area around the city, which is controlled by the Islamic State group (IS), said Al-Arbain mosque was dynamited on Wednesday.
The shrine is the reputed burial site of 40 early Muslim figures, including companions of Prophet Mohammed.
IS advocates a return to the origins of Islam but also considers worshipping at graves to be tantamount to idolatry and has blown up several revered shrines across the country.
Witnesses told AFP that IS gunmen set up the explosives inside the shrine on Tuesday and detonated them the next day.
"Yes, they have blow up this holy site," said Yahya al-Attawi, the imam of the main mosque in Tikrit, speaking from outside the city.
Elsewhere in the hometown of executed former president Saddam Hussein, IS also rigged the Green Church, a striking structure carved into the rock and first built in the seventh century.
Residents said many streets, homes and public buildings had been booby-trapped by the jihadists who have held the city for more than three months and fought off attempts by government forces to take it back.
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