It is the second best position Minh has held in his career. He was world No 5 in November 2010.
The top player in the latest rankings is Lee Chong Wei of Malaysia. He is followed by Chinese pair Chen Long and Chen Jin.
Japan’s Kenichi Tago remains fourth while China’s Du Pengyu takes fifth.
Minh has four days to recover from a calf injury before heading to Malaysia’s Maybank Open on January 15.