The Gloucestershire-based side were due to face League One side Blackpool on Saturday at 3pm at Bloomfield Road.
However, less than 24 hours before kick-off, the club announced that the fixture would not longer be going ahead due to the investigation.
A statement on their website on Friday night read: "Forest Green Rovers are aware of an FA investigation, meaning our FA Cup tie against Blackpool tomorrow is postponed.
"We will comply with the FA in their investigation and will provide a full update to supporters in the coming days once the investigation is complete.
"Forest Green Rovers apologises to both FGR and Blackpool fans who planned to attend tomorrow's fixture."
MORE ON FOOTBALL
Ten Hag uses stat to claim Onana is 'second best goalkeeper' - which puts Luton man top
Piers Morgan: Arsenal can win Champions League and Premier League if they sign one man
Meanwhile, the Tangerines also released their own response.
As well as confirming the game was off due to the investigation into their opponents, they said: "Blackpool Football Club would like to apologise to supporters for the inconvenience this has caused and is disappointed to be informed of this news at such short notice."
Forest Green, who boast ex-Watford striker Troy Deeney in their squad, beat Scarborough Athletic in the previous round in the first round replay following their initial 1-1 draw.
Last week, League One side Barnsley were expelled from this year's FA Cup.
Most read in EFL
I was play-off final hero but had to borrow money from loan shark to get out of contract
Barnsley winner against Wycombe rivals Mbappe equaliser vs Newcastle for bewilderment
Bellingham, Grealish plus Arsenal and Chelsea stars were part of vintage Championship year
Jobe Bellingham quietly building elite interest while brother Jude stars for Real Madrid
The Tykes were punished for fielding an ineligible player, leading to first round opponents, non-league Horsham, to re-enter the competition and take their place.