Around 40 fans walked out of the CNG Stadium or refused to watch the second half after the club banned the use of a drum due to noise levels affecting residents.
Town’s support base has had a burgeoning reputation across the National League North over the last two years after ramping up the atmosphere at the CNG Stadium.
An attendance of 728 was recorded for Kidderminster’s visit.
Town’s communications manager Daniel McGeachie said the action was taken after consulting with local residents.
McGeachie said: “We have taken on board residents’ complaints regarding loud drumming inside the ground and have agreed to silence it for evening fixtures.
“It goes without saying that we still encourage lively and vocal support of the team at every match.”
Weaver asked fans to get behind the squad ahead of the arrival of Darlington 1883, who have one of the biggest travelling supports in the National League.
The boss added: “They have a fantastic fan base and they will be out in force getting behind their team and I am sure our fans will be doing the same.
“They know what we are doing with our injury list. We just have to man up and deal with it.”
Meanwhile, the club has confirmed supporters will be segregated for Saturday’s clash with Darlington.