Sir John Milne, McAlpine's chairman, said the quarry products business had performed well in 1994, allowing the company to achieve a sale price over its basic asset value. The money will be used to reduce borrowings.
Following the deal McAlpine will have net cash of about £13m compared with borrowings of £30.2m at the end of December.
While Alfred McAlpine Minerals is a significant quarry operator in various regions, its UK market share is small. It is also seen as vulnerable to big changes in demand.
The stock market was unsurprised by the move, with the shares adding a penny to 164p.
McAlpine said its housebuilding division had an excellent 1994, with legal completions ahead of expectations.