Afghan embassy sources told BBC two staff members and a generic account received alerts from Google this month.
Last week Amnesty International detailed attempts to install malware on computers and phones of activists critical of Pakistan's military. The army did not comment on allegations intelligence services were to blame.
After the Google warning alerts were sent out, another Afghan diplomat's email account was hacked and made to send out emails, without his knowledge, containing suspicious attachments.
The emails purported to contain photographs of rallies by protesters known as the Pashtun Protection Movement (PTM). In fact, the attachments appear to contain malicious files, although it was not possible to download and examine them.
The PTM movement has accused the Pakistani military of committing human rights abuses in the country's fight against terrorism. Protests have been non-violent but controversial due to their unusually direct criticism of the Pakistani intelligence services.
A source in the Afghan embassy told BBC he was concerned that recipients of the emails sent out from the diplomat's account could believe the Afghan embassy was linked to the movement. The two countries regularly accuse each other of working to undermine the other's security.
The email was sent to addresses publicly linked to a number of political figures in Pakistan. They include a former information minister and a former law minister.
It was also sent to a former senator from a Pashtun nationalist party, Bushra Gohar. Ms Gohar told the BBC: "I know for a fact that all my accounts are being observed… this is condemnable." She added: "Parliament needs to form a committee and look into what is going on."
An employee of the Afghan embassy and a former member of staff were also both targeted by a fake Facebook profile linked to cyber-attacks.
