Lothian and Borders Police began the inquiry after they were contacted about the game between non-league clubs Hawick Royal Albert and Huntly on Saturday.
Bookmakers William Hill also said today they were looking at bets taken on the first round tie.
Huntly, of the Highland League, won the game 7-0, with the first goal coming from a penalty when a Hawick player was sent off for a handball near their own goal.
Hawick club secretary Douglas Purves confirmed an internal investigation had been launched into the match-fixing claim.
“The club will move into a full investigation. My intention is to go to the training ground tonight to interview all the players who were involved in the game,” Mr Purves said.
“There will be a full investigation by the club.
“The club didn’t know anything about it and can not make any statement until further notice.”
A spokeswoman for Lothian and Borders Police said: “We can confirm that we received a complaint and we are investigating.”
Graham Sharpe from William Hill said it was too early to say whether there had been any irregular betting patterns in connection with the game.
“We are going back and taking a look,” he added.
Mr Sharpe said bookmakers would not take bets worth thousands of pounds on Scottish Cup games such as this fixture.
A spokesman for the Scottish Football Association said: “We will co-operate fully with any investigation.”
According to a match report on the Huntly FC website, the winners had 36 attempts on goal with 19 shots on target.
Hawick, who were founded in 1947, are at the bottom of the East of Scotland League’s First Division.
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