Reuters verified the location of two video clips using the distinctive arches and buildings that match file images.
However, the semi-official Tasnim news agency denied Khomeini's house was set on fire, saying a small number of people had gathered outside the house.
The social media videos show dozens of people cheering as a flash of fire is sparked in a building.
Reuters could not independently verify the dates when the videos were filmed. Activist network 1500Tasvir said the incident occurred on Thursday evening in Khomeini's birth town of Khomein, south of the capital Tehran.
The house had been converted into a museum.
"The report is a lie," Tasnim said. "The doors of the house of the late founder of the great revolution are open to the public."
Khomeini died in 1989. His successor, Ayatollah Ali Khamenei, has been under intense pressure from nationwide protests calling for an end to rule hardline clerical rule since the death in September of Iranian Kurdish woman Mahsa Amini while in the custody of Iran's morality police.
Thousands of people took to the streets on Thursday in the latest round of protests after activists called for country-wide protests and strikes from Tuesday to Thursday.
The occasion was the commemoration of "bloody November" of 2019, when the security apparatus violently suppressed protests.
According to reports, there were protests in dozens of cities, some of which were violently suppressed.
Separate videos posted by 1500Tasvir purported to show marchers in several cities in Sistan-Baluchistan province, including the capital Zahedan, where protesters chanted "Death to Khamenei", and Chabahar, where demonstrators removed and trampled the sign of an avenue named after Khomeini.
On Friday, Tasnim reported pro-government demonstrators in the northeastern city of Mashhad, where two members of the Basij militia were killed on Thursday.
Late on Friday, protests continued in several cities and towns in the Kurdish-populated northwest, including Piranshahr, where demonstrators occupied a police station, according to a video posted by human rights group Hengaw.
Reuters with DPA
