People in the South Ham area of Basingstoke complained about the noise coming from the ground between 22:00 BST on Saturday and 08:00 on Sunday.
The club has apologised, blaming a wi-fi receiver picking up the frequencies of the radio systems of taxis.
Resident Leighton Oliver has criticised the club for not acting sooner to stop the noise.
He added it could be heard three miles away.
Another resident, who did not want to be named, told BBC Radio Berkshire he was woken by a "horrible scraping noise".
"It was like someone had put a microphone beside a really badly tuned radio," he said.
"It was so loud I'd be surprised if anyone got any sleep."
Basingstoke Town FC chairman Raffi Razzak said: "It's very unusual - it seems that the wi-fi in our PA box, which has been there for years for some reason, has started to pick up the frequencies of the radio systems of taxis.
"It was coming and going when a taxi passed with [its] music on.
"We never thought for one minute it could pick up signals from outside."
He said the system would be completely turned off when not in use in the future.
A Hampshire Police spokesman said officers had checked the premises after a call from a member of the public concerned that the social club may have been broken to.
Basingstoke and Deane Borough Council said its out-of-hours call centre received six calls about the noise.
"We will be speaking to the football club to clarify what exactly happened and the safeguards and procedures they have in place to ensure a situation like this doesn't happen again," a spokeswoman said.

The 24-year-old from Runcorn became Britain's first champion in the event's 17-year history with last year's win.
After taking gold in the season-opener in Switzerland, Coxsey reversed the outcome from the last event in China by pipping Janja Garnbret to gold.
Coxsey leads the Slovenian in the overall rankings, with four more events to take place before August.
Japan's Miho Nonaka claimed bronze, with Britain's Michaela Tracey 11th.
Sport climbing - which includes bouldering - is one of five new sports confirmed for the 2020 Tokyo Olympics.
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WATCH: How Shauna Coxsey became the UK's first bouldering world champion
Hundreds of people suffered a sleepless night when a football stadium's PA system played loud, distorted music.
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Shauna Coxsey continued her Bouldering World Cup title defence by claiming gold in the third event of the season.