Both clubs admitted charges relating to a failure to control their players and/or officials and/or supporters during the game on 14 September.
The two sides were also fined £150 by the Football Association and warned about their future conduct.
AFC Sudbury will now receive a walkover into the third qualifying round.
“We will now wait to receive the official judgement from the FA before considering whether to exercise our right to appeal”
Sleaford Town FC statement
Sleaford were leading 2-1 when players from the two sides clashed after a Huntingdon player was sent off following an altercation with a member of the home side's management team.
An FA hearing ruled on Thursday that both clubs failed to ensure players and/or officials and/or supporters conducted themselves in an orderly fashion and/or refrained from provocative and/or violent behaviour.
A Sleaford Town statement said: "It is with great disappointment to us that the FA has made the decision to remove both clubs from this year's competition.
"We will now wait to receive the official judgement from the FA before considering whether to exercise our right to appeal.
"Whilst naturally devastated with today's decision we would like to thank everyone who has offered their support through what has been a difficult time for Sleaford Town FC."
Lincolnshire club Sleaford and Huntingdon, from Cambridgeshire, both play in the United Counties League Premier Division, five tiers below the Football League.