Midfielder Daniel Thomas will now be subject to an internal investigation by the Welsh Premier League club over an allegedly homophobic tweet that was sent to Daley from his account.
Despite Thomas being suspended, club officials told the BBC that they believe the 28-year-old was victim of a "misguided prank" after he left his mobile unattended. The offending tweet has been deleted.
A club spokesman said: "Port Talbot Town Football Club can confirm Daniel Thomas has been suspended from all involvement with the club until we have carried out a full internal investigation.
"We were made aware to an offensive comment appearing on the Twitter feed of one of our players.
"Upon being informed of the matter, we immediately distanced ourselves from any offensive messages whilst investigating the matter further.
"Having spoken at length to the player in question, we believe he regrettably left his phone unattended and was the victim of a very misguided 'prank'."
The club said that both it and Thomas apologised "unreservedly" to Daley for the tweet, and in no way condoned the views it expressed.
Port Talbot chairman Andrew Edwards will meet with the club's players on Thursday, and remind them of the need for appropriate and responsible use of social media.
Daley has been subject to abuse from some quarters of the microblogging site ever since he came fourth with partner Pete Waterfield in the 10m synchronised diving on Monday (July 30).
In a separate incident this week, a 17-year-old Twitter user was arrested over a malicious tweet sent to the diver, understood to contain comments related to his late father.
The teenager was handed a harassment warning and bailed pending further investigations of his Twitter account.
Also today, Arsenal footballer Emmanuel Frimpong was fined £6,000 by the Football Association for posting a religious slur about Tottenham fans on Twitter.
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