By Agence France-Presse
The attack occurred a day after talks fell apart between the Taliban and Afghan representatives. No one claimed immediate responsibility and there was no immediate word on casualties.
"The information that we have is four attackers have placed themselves near the communication ministry and are engaged in gun battles with the Afghan security forces," Amanduddin Shariati, a security official in Kabul told AFP.
Interior ministry spokesman Nasrat Rahimi said an explosion was heard near the communication ministry around 11:40 am (0710 GMT), followed by sporadic gunfire.
Local television footage showed a small plume of smoke near the ministry, and people climbing out the windows on a lower level.
Intermittent firing could still be heard more one hour after the blast, and the area had been cordoned off by security forces.
The communication ministry is located in downtown Kabul, about two kilometres (1.25 miles) from the green zone. It is the city's main commercial area and has several large hotels.
The communication ministry itself is an 18-storey building, thought to be the tallest building in Kabul.
The explosion comes a week after the Taliban announced their annual spring offensive and amid ongoing fighting across Afghanistan.
The Afghan branch of the Islamic State group has also previously carried out multiple deadly attacks in Kabul.
The capital has in recent weeks enjoyed a period of relative calm, after a horrific year last year in which it saw a string of attacks including a massive bomb that was concealed in an ambulance and killed more than 100 people.
This week in the Qatari capital Doha, a summit planned between the Taliban and officials from across Afghanistan fell apart at the last minute due to bickering over who should attend the conference.
The collapse comes at a critical time and amid continued bloodshed in Afghanistan, where the Taliban now control or influence about half of Afghanistan and 3,804 civilians were killed there last year, according to a UN tally.
Taliban officials are separately negotiating with the United States, which wants to forge a peace deal with the militants.