One bomber died in the attack in the Black Sea city of Ordu on Friday, and the other was injured.
CNN Turk said a third person was also injured in the blast in the toilets of a Quran teaching facility at the mosque. Television images showed a building that appeared to have been gutted.
There was no immediate claim of responsibility.
Police in Ordu were not immediately available for comment.
Separately, a bomb exploded in the road in Diyarbakir in Turkey's southeast, injuring three people including two children. Two of the injured were in a car belonging to local authorities, security officials told Reuters.
Security officials said the bomb was timed to attack army personnel.
There have been a number of bombings and violent protests in Turkey's southeast in recent days, leaving scores dead.
The attacks came after a bomb ripped through offices of the ruling Justice and Development Party (AKP) on the outskirts of Istanbul on Wednesday, injuring two people.
Last week another bomb attack in Turkey's largest city, Istanbul, which killed one person, was blamed on Kurdish militants.
The Kurdistan Liberation Hawks (TAK), which has ties to the Kurdistan Workers Party (PKK) said it carried out the Istanbul blasts.
Turkey blames the PKK, which is viewed as a terrorist organisation by the European Union and the United States, for the deaths of more than 30,000 people since it launched an armed struggle in 1984 for a Kurdish state.
Militant groups including Kurdish separatists, Islamists and ultra-leftists have carried out attacks on civilians, security and military targets in Turkey in the past.
A series of devastating bombs went off in Istanbul in November 2003, targeting British and Jewish sites and killing more than 60 people.