The 27-year-old smashed his own national record, and was just 72cm short of the World Record, set by three-time Olympic champion Jan Železný in 1996.
The throw gave Vetter the win at the Kamila Skolimowska Memorial meeting in Poland on Sunday (6th September). Home hope Marcin Krukowski finished second with 84.62m.
Vetter, who finished fourth at the Rio 2016 Olympic Games before winning the 2017 World Championships in London and claiming bronze at the 2019 Worlds in Doha, threw 94.84 with his next attempt under the covered roof in Chorzow, which is the sixth longest distance ever recorded.
In an interview trackside moments later, the German revealed that the achievement came in the city where his grandfather was born, and suggested that had it been in an "open" stadium the huge throw would have broken the world record and travelled "over 100m".
Meeting records fall
There were several other meeting records in the track and field events in Chorzow.
Poland's Maria Andrejczyk won the women's javelin with a new mark of 65.70m, in front of a home stadium full of cardboard cutouts of fans due to coronavirus restrictions preventing spectators attending the event.
Brit runner and fellow Rio 2016 Olympian Laura Muir won the women's 1500m in a time of 3:58.24.
The men's shot put event in Chorzow was won by American Ryan Crouser, who bettered the meeting record with each of his first three throws. The Rio 2016 champion finished with a best of 22.70m to continue his excellent 2020 season.
It came on a weekend where several world records were broken in a number of other events across Europe, as Peres Jepchirchir smashed the women's half marathon World Record in Prague on Saturday, after Sifan Hassan and Mo Farah broke the women's and men's one hour world records on the track at the Diamond League event in Brussels.