Officials said 34 died in the Sarobi district alone, around 65 km (40 miles) east of the Afghan capital Kabul.
Pakistan’s biggest city Karachi was also badly affected, with at least 16 killed after days of flooding.
The region has suffered devastating floods during the monsoon period for the past three years.
Afghan officials said that emergency teams and supplies were being dispatched to affected areas.
Hundreds have been displaced in eastern areas of Afghanistan and hundreds of hectares of farmland destroyed, Ghulam Farooq, the head of emergency operations for Afghanistan’s National Disaster Management Authority, told AFP news agency.
The floods have caused extensive damage to property in both countries.
The Pakistani army was called in to help the clean-up in Karachi, where local media reports say sewage and rainwater have blocked some of the main roads.
The fatalities in the city have been mostly due to electrocution or collapsing roofs and walls. The floods are also reported to have left many areas of the city without power.
In Pakistan’s north-western Khyber Pakhtunkhwa province, many houses were swept away by the torrent, officials said.
Pakistani disaster response officials have warned that more rain may be on the way over the coming days.
In 2010, Pakistan was hit by the worst monsoon floods in 80 years. Almost 1,800 people were killed and 21 million people affected.
Flooding in each of the following two years also left hundreds dead.