Speaking on Musk's infamous marijuana consumption during "The Joe Rogan Experience" podcast in September, the NASA chief said 'that was not appropriate behaviour' and people will not be seeing that again, The Atlantic reported on Thursday.
Bridenstine said he has spoken with Musk recently that he does not want NASA contractors engaging in questionable behaviour.
"We've had a number of conversations," he said.
"I will tell you, he is as committed to safety as anybody, and he understands that was not appropriate behaviour, and you won't be seeing that again," Bridenstine told reporters at NASA headquarters in Washington on Thursday.
NASA along with Musk's SpaceX and Boeing is developing transportation systems that would allow the US to fly astronauts from American soil for the first time since the space shuttle was retired in 2011.
"The leaders of these organisations need to take that as an example of what to do when you lead an organisation that's going to launch American astronauts," Bridenstine said.
The warning comes about a week after reports suggesting that NASA would conduct reviews of workplace culture at both SpaceX and Boeing.
"NASA will be conducting a cultural assessment study in coordination with our commercial partners to ensure the companies are meeting nasa's requirements for workplace safety, including the adherence to a drug-free environment," the agency had noted in a statement.
On Thursday, Bridenstine said he personally ordered the reviews.
He attributed his decision to several tragedies in NASA history, including the Apollo 1 fire in 1967, when three astronauts were killed during a ground test, and the two space-shuttle disasters (Challenger in 1986 and Columbia in 2003), which together killed 14 people.
A spokesperson for SpaceX declined to comment on Bridenstine's remarks, the report said.
Last week NASA announced that the first uncrewed test by SpaceX is tentatively scheduled for January 7, but Bridenstine said on Thursday that the date is unlikely to stick and may slide into spring.
Crewed test flights are expected next summer but that timeline is also likely to change, the report said.