The NGO said it took the allegations seriously but said it had been unable to confirm the claims, made by anonymous whistleblowers, and urged anyone with information to come forward.
A former employee based in MSF's London office told the BBC she had seen a senior staff member bring girls back to MSF accommodation while posted in Kenya.
“The girls were very young and rumoured to be prostitutes,” she said, adding that it was “implicit” that they were there for sex.
She said some of the older, long-standing male aid workers took advantage of their positions.
“I felt that, with some of the older guys, there was definitely an abuse of power,” she said.
“They'd been there for a long time and took advantage of their exalted status as a Western aid worker.”
She questioned what the charity knew, saying: “There's definitely a feeling that certain predatory men were seen as too big to fail.”
Another female employee who worked with HIV patients in central Africa said the use of local sex workers was widespread.
“There was this older colleague, who actually moved a woman into the (charity) compound. It was pretty obvious that she was a prostitute but he'd call her his girlfriend,” she said.
A third whistleblower described how a senior colleague boasted of trading medication for sex with girls in Ebola-hit Liberia.
“He said, 'Oh it's so easy. It's so easy to barter medication with these easy girls in Liberia',” she told the programme.
“He was suggesting lots of the young girls who had lost their parents to the Ebola crisis, that they would do anything sexual in return for medication.”
In a statement, the agency said, “We do not tolerate abuse, harassment or exploitation within MSF.”
“We are sorry for any instances where people have been subjected to harassment, abuse or otherwise mistreated and/or felt that it was not adequately dealt with.”
The allegations follow a crisis at British charity Oxfam over claims that its aid workers used prostitutes while stationed in Haiti after the devastating 2010 earthquake.
“We know that MSF is not immune to these issues and we take any reports seriously,” the charity's statement said.
But it said that “based on the information provided, we have been unable to confirm the specific allegations”.
“We would urge anyone with any concerns to report them via MSF's confidential whistleblowing mechanisms so that we can take action,” it said.
The charity said it had complaints procedures in place but “we know we need to do more to ensure that they are known, trusted and used by the people who need them”.