Liverpool midfielder Henderson won the men's award ahead of second-placed Raheem Sterling and third-placed Harry Kane.
Sterling admitted on Instagram on Tuesday he and Gomez "had words" when they met up at the England camp the day after Liverpool's 3-1 win over defending champions Manchester City which left the latter nine points adrift of Jurgen Klopp's side.
England eased to a 6-0 victory over their hosts in the Bulgarian capital on Monday but the game was blighted by offensive chants, forcing the match to be halted twice in the first half.
Captain Ronaldo, making his 160th international appearance, scored four as Portugal won 5-1 in Vilnius and strengthened their position in Group B after a sluggish start.
England’s 5-1 rout of Montenegro in Podgorica in March was soured by racist abuse from fans and the hosts were ordered to play their next European competition match behind closed doors as part of sanctions handed out by Uefa.
England play their Nations League semi-final against the Netherlands on 6 June and Southgate is hopeful the striker will complete a full recovery over the next three weeks.
Tottenham Hotspur full-back Rose was among the players who were victims of offensive chanting when they played for England in Montenegro last month in a Euro 2020 qualifier.
Mbappe scored one and set up two more as the reigning world champions crushed Iceland 4-0 at the Stade de France to move top of Group H in Euro 2020 qualifying.
City and Liverpool are vying for the title, while Spurs face competition from Manchester United, Arsenal and Chelsea for a top-four finish.
Speaking ahead of France’s Euro 2020 qualifier against Moldova on Friday, the Manchester United midfielder also said Sterling was unfairly criticised for what he does off the field.
Gordon Banks' family said he had passed away in his sleep.
Rooney will start on the bench before entering the field for his 120th and final cap in the international at Wembley Stadium.
