Ian Blackford told Sunday Politics Scotland it was not a matter for him to review complaints made about Joanna Cherry.
He said authorities at Parliament would investigate the matter.
Mr Blackford said: “These are not matters for me as parliamentary leader.
“These are matters for the parliamentary authorities.
“One of the things I do want to see is if people do bring forward allegations that they are treated with respect and indeed that MPs are treated with respect as well.
“We have a duty as a party to make sure that we care for all our staff and we care for all our MPs.”
Allegations of bullying against the SNP’s justice and home affairs spokeswoman emerged in newspapers over the weekend.
Ms Cherry has not formally commented.
She tweeted: “Lies are being told about me in some newspapers today.
“At present I’m not able to give my side of the story. I hope to be in a position to do so soon.
“Meantime I’m overwhelmed by the support from constituents, @theSNP members & #Yessers. Thank you.”
Scottish Conservative deputy leader Jackson Carlaw said: “It’s clear today that the SNP is in open warfare.
“Nicola Sturgeon needs to exercise some of her much diminished authority and fast.”