Monnin renounced her Miss Pennsylvania crown earlier in the week, accusing the recent Miss USA beauty pageant of being rigged.
As chairman of the pageant, which is a subsidiary of the Miss Universe Organisation, Trump made a public response, warning Monnin that she had 24 hours to retract her statement if she wanted to avoid legal action.
According to TMZ, the 27-year-old beauty queen failed to retract her allegation, and has now been slapped with two lawsuits.
The two suits accuse Monnin of breach of contract and defamation, and lawyers say that they are seeking "significant damages" from the former pageant contestant.
A private arbitrator is currently examining both court filings.