Heavy rain in Somerset has ruined the playing conditions and match officials took the decision to postpone the game ahead of the 5.30pm kick-off.
Several other New Year's Day matches have fallen foul to the wet weather across the country.
Bristol Rovers v Cheltenham, Newport County v Oxford United, Northampton v Chesterfield and Exeter v Wycombe - all in League Two - were postponed due to waterlogged pitches.
Staff at Bristol Rovers' Memorial Ground had declared their pitch playable on New Year's Eve but the surface failed a 10am inspection on Wednesday morning.
"Referee Iain Williamson inspected the pitch this morning, and decided that the match should not go ahead," read a news update on the club's official website.
"There were puddles of standing water on the surface, and with bad weather expected to continue all day, the match official took the decision to call the game off early."
Gillingham's game at Stevenage was the first League One contest to fall foul of the weather just after midday.
The weather has also led to the postponement of four games in the Skrill Premier League with Braintree v Cambridge, Hereford v Kidderminster, Salisbury v Woking and Welling v Dartford all called off.
Bad weather prompted the other New Year's Day postponement in the Football League, with stormy conditions causing floodlight damage at Leyton Orient, who were due to host Bristol City in League One.
No new dates for any of the postponed matches have been announced so far.