Another Russian news agency, RIA, quoted Armenia's Security Council as saying the incident took place on Sunday but the Azeri troops had since left.
There was no immediate reaction from Azerbaijan.
Pashinyan did not say on what scale the incursion had taken place but told a security council meeting that he had dismissed minister Arshak Karapetyan over the incident, Reuters reported.
TASS news agency said Armenia had reported the incident to Russia and the Collective Security Treaty Organization, a military alliance of post-Soviet states.
Armenia and Azerbaijan fought a 44-day war last year over the enclave of Nagorno-Karabakh that killed at least 6,500 people and ended in a decisive victory for Azerbaijan.
The fighting ended with a Russian-brokered peace deal under which Moscow deployed 1,960 peacekeepers to the region for an initial five-year period.
But tensions remain high between the two former Soviet republics and the accord left many questions unresolved, including the legal status of Nagorno-Karabakh and the Armenians who live there, who numbered up to 150,000 before the war.