Lynch and other NFL players have taken a knee or sat during the anthem as a way to protest police brutality and racial inequality in the US Trump has called their actions disrespectful to the country and in the past has said protesting players should be fired.
After sitting during the "Star-Spangled Banner," the five-time Pro Bowler rose for the Mexican National Anthem while getting equipment put on. The Raiders went on to lose 33-8 to the New England Patriots at Estadio Azteca.
"Marshawn Lynch of the NFL's Oakland Raiders stands for the Mexican Anthem and sits down to boos for our National Anthem," Trump tweeted. "Great disrespect! Next time NFL should suspend him for remainder of season. Attendance and ratings way down."
NFL spokesman Brian McCarthy told Reuters the league will not move to suspend Lynch, who has sat during the anthem all season long.
"That's not something that's under consideration," he said in an email on Monday.
"We've said that we would like to see everyone at our games stand for the anthem. We have been working with players on platforms that highlight social issues and promote initiatives that make our communities better."
Seattle Seahawks running back Marshawn Lynch sits at his podium during media day for Super Bowl XLIX (Reuters)
Image credit: Eurosport
NFL television ratings have fallen this year. Through the first six weeks of the NFL season, total viewership of games is down 7.5 percent, compared with the first six weeks of 2016, according to ESPN.
But it is not known whether the lower ratings are linked to NFL player protests or are part of a wider trend of people using other platforms instead of watching television.
A Super Bowl champion in the 2013/14 season with the Seattle Seahawks, Lynch joined the Raiders this year after a brief retirement following the 2015 season.
He earned a one-game suspension last month for running onto the field and pushing an official during a quarrel between players during the Raiders win over the Kansas City Chiefs.
The White House, the NFL Players Association and the Raiders did not respond to requests for comment.