A gunman entered a Shia Muslim mosque in Kabul before opening fire and detonating an explosive, killing at least 39 worshippers.
An attack on a Sunni Muslim mosque in Ghor province killed 20 people.
No groups have so far said they carried out the attacks but so-called Islamic State (IS) has previously targeted Shia mosques across Afghanistan.
The new attacks bring to at least 176 the number of people killed in bomb attacks across the country this week.
One eyewitness told the BBC that the scene at Kabul's Imam Zaman mosque, in the west of the city, looked like a "front line".
Another witness, Mahmood Shah Husaini, said people had been praying when the bomber detonated his explosives.
The attacker is reported to have opened fire as worshippers gathered for Friday prayers, before detonating a bomb.
Kabul police spokesman Basir Mojahid confirmed the incident at the Shia mosque in Kabul, but did not give further details.
A spokesman for the Afghan interior ministry said investigators were working at the scene to determine the "nature of the explosion," AFP news agency reports.
The attack on the Sunni mosque in Ghor, central Afghanistan, also killed a pro-government militia commander, according to reports.
Details of the attacks remain unclear and the number of casualties is likely to rise. Dozens of worshippers were also injured, Afghan's health ministry said.
Friday's attacks come just days after police in Kabul said they had arrested a would-be suicide truck bomber, averting a major incident.
In August, more than 20 people were killed in a bomb attack against worshippers in Kabul. IS, a Sunni Islamist militant group, said it had carried out the attack.
A truck bomb in the Afghan capital in May killed more than 150 people and wounded some 400 more, most of them civilians. No group claimed to be behind that attack but the US-backed Afghan government accused the Haqqani group, an affiliate of the country's biggest militant group, the Taliban.
Afghanistan has seen a spate of suicide attacks and bombings in recent months.
There have been four major attacks on Afghan security forces this week alone:
On Thursday, 43 Afghan soldiers were killed after two Taliban suicide bombers in Humvee armoured vehicles destroyed a military base in the southern province of Kandahar. Two police officers were also killed in in Ghazni province
On Tuesday, Taliban suicide bombers and gunmen killed at least 41 peoplewhen they stormed a police training centre in the eastern city of Gardez while two police officers
Also on Tuesday, at least 30 people died in car bombings in Ghazni
Afghanistan's army and police have suffered heavy casualties this year at the hands of the Taliban, a Sunni group who want to re-impose their strict version of Islamic law in the country.
Photo copyright: REUTERS (Caption: Security forces guarded the scene after Friday's Kabul attack)