Both men featured for Martin O'Neill's side as they were beaten by Scotland on Friday, but they have been released ahead of Tuesday's clash in Dublin.
Keane only played the final 12 minutes in Glasgow, but was unable to find a way through as Ireland lost their advantage in Group A of Euro 2016 qualifying, with Scotland moving level with them on seven points.
He will now return to the United States to join up with LA Galaxy, enabling him to prepare for the MLS Cup western conference final first leg with Seattle Sounders on November 23.
O'Neill opted to start Gibson in central midfield alongside Jeff Hendrick, with the Everton man withdrawn after 68 minutes for Stephen Quinn.
The 27-year-old picked up a minor knock to his knee and will return the Premier League side for rehabilitation.