Mr Henry is the MSP for paisley South and is also the deputy justice minister. He has written to SFA chief David Taylor, and if he is not satisfied with the reply could get the Scottish parliament involved.
Saints chairman Stewart Gilmour was supposed to meet Taylor today to discuss the fine, and has not ruled out taking legal action.
Saints were fined after failing to name two under 21 outfield players for the recent Scottish Cup game against Spartans, despite referee Charlie Richmond saying no error had been made.