According to Pakistani sources familiar with the matter, the staff members rushed to meet an injured pedestrian and then tried to leave.
A first police report obtained by CNN said the two men had been arrested for “reckless and outrageous driving”.
Sources said the two were employees of the Indian High Commission in Islamabad, not diplomats. The source added that the two men were released following a “special request from the Pakistani Foreign Ministry” and were handed over to a senior Indian High Commission official because they are still subject to diplomatic immunity.
After their arrest, police discovered that the men had diplomatic immunity.
The incident comes at a time of tension between the two nuclear-armed neighbors.
Pakistan’s foreign ministry said the decision to declare the two men non grata was accompanied by a negatively planned and orchestrated media campaign, which is part of persistent anti-Pakistani propaganda.
He said the Indian envoy had been summoned and issued his own decree, condemning the “unfounded Indian allegations”.
Diplomacy between India and Pakistan is common, especially when tensions in the disputed region of Kashmir are high or when there are military operations or combat attacks.
In August last year, the Indian government stripped Kashmir of its autonomy and special status, prompting Pakistan to downgrade diplomatic relations and suspend bilateral trade with India.
The two countries have a long-running dispute over Kashmir for more than 70 years.
On Monday, Pakistan tried to frame the move against top officials as an attempt by India to divert attention from domestic political issues and the situation in Kashmir.
“It would serve the PM Modi government and the Neighborhood Policy to realize that India’s neighbors have far fewer problems than their own domestic inadequacies, failures and fascism,” he wrote on Twitter.
Sophia Saifi reported from Islamabad, James Griffiths from Hong Kong. CNN’s Adeel Raja, Vedika Sud and Helen Regan contributed to the report.