Lancashire Police received a report of "an altercation" between two men outside the Bloomfield Road ground at about 11:30 BST on 25 June.
The firearm was not used to threaten anyone and "no criminal offences were committed", police said.
Blackpool FC said neither Mr Oyston, 48, nor the club would be commenting.
Police said a 48-year-old man was "spoken to" about carrying a firearm in public.
A spokesperson said the matter had been concluded.
Blackpool chairman Karl Oyston has been spoken to by police about carrying a firearm outside the football club's stadium, the BBC understands.