The attacker detonated his suicide vest in Imam Zaman mosque in the early evening, police said.
Abdulhai Khatebi, Ghor provincial spokesman, said the attacker detonated his suicide vest during worship services in the late afternoon. The mosque is in the province's Doleena district.
The US State Department condemned the attacks in a statement Friday, as well as others that took place in Afghanistan earlier in the week.
"In the face of these senseless and cowardly acts, our commitment to Afghanistan is unwavering," said Heather Nauert, spokeswoman for the State Department. "The United States stands with the government and people of Afghanistan and will continue to support their efforts to achieve peace and security for their country."
Sectarian tensions have raged for some time between members of the Sunni and Shiite denominations of Islam. But there were no immediate claims of responsibility for Friday's attacks . ISIS has claimed responsibility this year for other attacks on Shiite mosques.
The Taliban claimed responsibility for that attack, according to a statement from the group's spokesman, Qhari Yosouf Ahmadi.
Taliban raids on Afghan military installations aren't uncommon. In April, a deadly raid on a northern army base left as many as 140 feared dead. That attack was revenge for the deaths of two Taliban officials in the region, a spokesman for the group told international media.