It is understood the allegations concern a 22-year-old SNP employee with whom the MP was drinking in Strangers bar in Westminster in January 2020.
A complaint was reportedly made against the MP in March.
It follows claims made against Patrick Grady, the party's former Chief Whip, earlier this year.
Mr Grady has stepped down from his Chief Whip role while the investigation is ongoing.
Responding to the allegations towards Ms Gibson, the SNP told the BBC individuals were entitled to have complaints dealt with confidentially and it would be inappropriate to comment further.
Ms Gibson has been the MP for North Ayrshire and Arran since 2015.
She recently became the SNP's spokesperson for housing, communities and local government.