The club reported the death threat against manager Darren Kelly, to Greater Manchester Police after receiving a letter on Monday.
Police said a 27-year-old man and 42-year-old man had been arrested on suspicion of making threats to kill.
The force said it was expecting to make further arrests and called on one man in particular to come forward.
35-year-old Darren Kelly, who was appointed as Oldham manager last week, has had to deny claims he supported the IRA after he reportedly called Sinn Fein politician and Northern Ireland Deputy First Minister Martin McGuinness a "legend" on Twitter.
Kelly, who is from Derry, made the comments after Mr McGuinness retweeted a photo of him meeting the Oldham boss's mother at an event marking the 43rd anniversary of Bloody Sunday in Derry.
Police said the letter sent to the club made some extremely serious threats and they are treating the matter with the utmost seriousness.
They also said vitriolic comments made on social media would form part of the investigation.