The NUM said it was "deeply shocked and concerned" by the attack at the member's house in Bapong village, near Brits. It called on law enforcement to "hunt down the perpetrators and arrest them".
Local South African media reported the chairman subsequently died in hospital.
The NUM and rival union the Association of Mineworkers and Construction Union (AMCU) have been involved in a drawn-out turf war in the area, with members of both unions attacked last year.
The NUM said in late-November that two "alleged" AMCU members had been arrested for killing an NUM branch leader, in April last year, in Mpumalanga.
Also in November, AMCU national organiser Dumisani Nkalishana said NUM members were killing its members because "they realise we are solid on our stance to protect workers".
The union accused the South African police service of colluding with the prosecution in December when two suspects arrested for allegedly killing AMCU members were released on technicalities.
Lonmin has seen no end of labour-related trouble, with its Marikana mine the scene of mass violence in August 2012 when 34 striking miners were shot dead by police.
The platinum mines will soon be the worry of someone else, with Sibanye-Stillwater (SJ:SGL) having made an all-share offer to buy Lonmin in mid-December via a scheme arrangement between the latter and its shareholders.
