Football's governing body said it was
looking at several potential breaches of its disciplinary code including the
misconduct of players and officials, and discrimination.
FIFA referred to "incidents"
during the group stage game, without saying what they were.
Fans during Friday's match in Qatar, which Switzerland
won 3-2 to progress, were told to "stop all discriminatory chants and
gestures".
It was not immediately clear what triggered
the announcement but it followed a confrontation between Swiss captain Granit
Xhaka and Serbia's players.
The flashpoint in the second half drew in
Switzerland forward Breel Embolo and Serbia substitutes ran onto the pitch at
Stadium 974 to remonstrate with Swiss players before the referee brought the
situation under control.
Xhaka comes from a family with roots in
Kosovo, the former Serb province with a majority ethnic Albanian population.
Serbia were already being investigated by
FIFA after the team hung a controversial flag in their changing room before
they lost to Brazil in Qatar.
The Kosovo football federation filed a
complaint with FIFA after photos showed a version of the Serbian flag with a
map that depicted Kosovo as part of the country and included the slogan
"there will be no surrender".