Weddle, one of the team's best players, has also been banned from attending San Diego's final NFL game of the season.
The 30-year-old chose to remain on the field instead of returning to the locker room at the end of the half.
Head coach Mike McCoy said in a statement that it was an "organisational call".
Weddle, who has played 137 games in a nine-year stint with the Chargers, was watching his seven-year-old daughter Brooklyn dance in a programme sponsored by the team's cheerleaders.
He was not the only player with a child performing, but was the only one who did not join his team-mates and coaches at half-time in last week's 30-14 victory over the Miami Dolphins.
McCoy added: "We have a club policy here and there are certain things we have to do at half-time to make adjustments and things like that."
Weddle, a free safety, was placed on the injured reserve list and told he will not be allowed to travel with the team for the season-ending game in Denver on Sunday.
He is set to become an unrestricted free agent this spring.
The San Diego Chargers have fined Eric Weddle $10,000 for watching his daughter perform a half-time routine with the team's junior cheerleaders.