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Richard Worth served as a minister outside Key's cabinet, holding the portfolios of internal affairs and land information.
No details of the investigation were released by Key but police confirmed they were conducting a preliminary investigation into an allegation against a member of parliament.
Key told reporters Wednesday that Worth's resignation was related to a criminal investigation but he refused to give any details.
He said he had accepted Worth's resignation on Tuesday night, adding he would have sacked the minister if he had not offered to quit.
"He advised me of some private matters in respect of which he felt it appropriate that he should resign as a minister," Key said earlier in a statement.
"I will not be making further comment on the matters he has advised me about."
Worth was also tightlipped about the reasons for his resignation.
"It is with deep regret that I have resigned my role as a minister," he said in a statement.
"I am resigning from the role for personal reasons."
"I will not be making any further comment to the media."
Worth is the first minister to resign since Key's centre-right National Party swept into government in elections in November, ending the nine years in power for Helen Clark's Labour Party.
