The visit comes after Iran's foreign ministry confirmed this week that exchanges of proposals with the US are continuing "through Pakistan".
Iran is reviewing a new US proposal aimed at ending the conflict, foreign ministry spokesman Esmail Baghaei said on Thursday.
There is a sense of optimism within Pakistani security circles that a preliminary agreement between the US and Iran is within reach.
Sources said Munir had been due to travel to Tehran on Thursday but waited for the go-ahead from the Iranian negotiators that an initial agreement could realistically be reached.
It is not known exactly which points are currently under discussion.
Munir is said to have good contacts with US President Donald Trump and is seen as a mediator between the warring parties.
Pakistan's Interior Minister and Munir confidant Mohsin Naqvi is already in Tehran.
He has met Iranian Foreign Minister Abbas Araqchi several times in recent days for talks, Iranian news agency Tasnim reported.
Qatar and Pakistan recently submitted a revised proposal for an agreement together with other partners to bridge differences between the US and Iran, according to the US news portal Axios.
US Secretary of State Marco Rubio expressed cautious optimism on Thursday about diplomatic efforts to end the Iran war.
Speaking ahead of his departure for a NATO meeting in Sweden, he said he believed progress had been made.
Baghaei said on Friday a Qatari delegation was currently holding talks with Iran's foreign minister, adding that Pakistan remained the main mediator in the negotiations.
with EFE, DPA and AP
