Minihan, 28, began his career with Rochdale, making one senior appearance. In 2012, Minihan made 14 appearances on loan at Droylsden. In 2013, Minihan was released from Rochdale and signed for Loughborough University FC in the Midland Football League. In 2014 he captained Loughborough University to 2-0 loss against a Manchester United Youth XI.
After two years with Loughborough, Minihan made the move to the National League North side Worcester City. In his first season with the club, he was named young player of the season and player’s player of the season.
In June 2016, the defender turned down a one-year extension with Worcester and joined Stockport County, also in the National League North. Minihan won the young player of the year award in his first season and was rewarded with a two-year contract. The defender made almost 200 appearances during his time with Stockport and played a part in their National League triumph last season.