Regulator Ofcom ruled the performance, by Alexandr Magala of Moldova, was "in line with audience expectations".
It also rejected suggestions the act might lead to copycat behaviour.
"The repeated warnings and clear references to the inherent danger of the act meant it was very unlikely that audiences would attempt to copy it."
Magala is no stranger to the ...Got Talent format, having previously appeared on the US, French, Italian, Russian and Ukrainian versions of the show.
The 26-year-old also performed at the opening ceremony of the Winter Olympics in Sochi in 2014 prior to his ITV debut on 9 April.
Audience members screamed and covered their eyes as the Magala slid down a pole with a sword lodged in his mouth, coming to a stop an inch above the ground.
"I actually thought you were going to die," judge Simon Cowell admitted after the act was put through to the next round of the competition.
The impresario later described Magala's oesophageal exertions as "the most dangerous act... ever seen on Britain's Got Talent".
The same programme drew three complaints over its language, another three relating to animal welfare and another related to "generally accepted standards".
These complaints will also not be investigated, according to the media regulator's latest broadcast and on demand bulletin.
ITV show Britain's Got Talent will not be investigated by the broadcasting watchdog over a sword-swallowing act that drew 33 complaints.