Mujati, 26, made the allegations on Twitter on Saturday morning. He later removed the postings, in which he claimed the remarks had come from Leinster prop Heinke van der Merwe and lock Steven Sykes during the pre-season match at Donnybrook.
It is understood that Van der Merwe and Sykes deny the allegations.
The only comment the Irish province would make was in a statement which said: "Following allegations made by a Northampton Saints player this morning via his personal Twitter account, Leinster Rugby are holding a full internal investigation.
"The managements of both teams are in close communication and hopefully the matter will be resolved as soon as possible.
"No further comment will be made at this time until that resolution has been reached."
Zimbabwe-born Mujati, who has won 12 caps for South Africa, was clearly upset when he posted on the social networking site.
A Northampton spokesman said: "The club takes any allegations like this very seriously. We will be talking to the player concerned about it and contacting Leinster.
"We will not make any further comment at this time."
The Rugby Football Union have confirmed that because the alleged incident took place on Irish soil it falls outside of their jurisdiction.
The Irish Rugby Football Union have said they are in touch with Leinster and Northampton on the matter.
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