Former midfielder Michael Carrick, who was on Solskjaer's coaching staff will be in temporary charge, starting with a trip to Spain for a Champions League match at Villarreal in the group stage
Watford dominated the first half and thoroughly deserved their two-goal lead at half-time, courtesy of goals from Joshua King and Ismaila Sarr.
The Norwegian boss is under intense pressure after a 5-0 home thumping by Liverpool and a one-sided 2-0 defeat at the hands of Manchester City on Saturday.
West Ham boss David Moyes strode triumphantly around the London Stadium pitch soaking up the acclaim from jubilant fans after a 3-2 win against Liverpool.
United have now won just one of their last six Premier League games and could finish the day 11 points off the top of the table should Chelsea beat Burnley at Stamford Bridge.
Liverpool recorded their record victory at Old Trafford in a 5-0 thrashing two weeks ago to leave Solskjaer clinging onto his job as United boss.
The 36-year-old also scored late winners at home to Villarreal and Atalanta, when United came from 2-0 down to win 3-2 two weeks ago.
Solskjaer admitted one good game would not silence United's doubters and challenged his team to prove in Italy that they could perform consistently.
Ole Gunnar Solskjaer made a change to the team's formation, switching from a 4-2-3-1 to a 3-4-1-2, the side led by a strike partnership of Cristiano Ronaldo and Edinson Cavani.
Solskjaer is fighting to keep his job heading to Tottenham this weekend and something needs to drastically change if he is to engineer another turnaround in his turbulent three years at United.
The squad had a planned rest day on Monday before they reported back to the training facility to see Solskjaer as expected on Tuesday.
United are already eight points off the pace at the top of the table and there is a growing consensus that they need a coach to match the calibre of Liverpool, City and Chelsea.
For the first time in Premier League history, United trailed 4-0 at half-time and failed to score in a hopelessly one-sided contest.
The season is young — United has only played 11 games — but key issues haven't been fixed: an imbalanced midfield, an attack relying on individualism over any coherent plan, sloppiness in defense.
United spent £73 million to sign Jadon Sancho from Borussia Dortmund in July but Ronaldo's return relegated Sancho's signing to the shadows.