Frants Nielsen (22 January 1874 – 6 June 1961) was a Danish sports shooter who competed in the 1912 Summer Olympics. He was born in , Purhus Municipality, and died in Randers. In 1912 at the Stockholm Games he participated in the following events: * 50 metre team small-bore rifle – fifth place * 50 metre rifle, prone – 26th place * 50 metre pistol – 40th place * 300 metre free rifle, three positions – 46th place