Manager Louis van Gaal confirmed their absences at his pre-match briefing on Friday, saying that 19-year-old James Wilson, who has only played for eight minutes in the league this season, would lead the front line.
But, Van Gaal added that Wilson would not play for the whole match at Vicarage Road because he has "a lack of match rhythm."
Rooney, who scored his 51st goal for England when they beat France 2-0 on Tuesday, has not trained since because of illness, though Van Gaal hopes he will be fit for United's Champions League match against PSV Eindhoven next week.
Martial, who also played in Tuesday's international at Wembley, left the stadium on crutches after taking a heavy blow to the top of his foot.
Carrick suffered an ankle injury when England played Spain last Friday while Fellaini will miss his second successive league match after picking up a leg injury.
Van Gaal added that France international Morgan Schneiderlin and Germany's Bastian Schweinsteiger could both play against Watford, despite being involved in the France-Germany friendly in Paris during last week's terror attacks which left at least 129 people dead.
"I think for every human being in this world, it was a big blow," so I don't think I have to mention what our discussions were, but Schweinsteiger and Schneiderlin can play," he said.
United go to Watford fourth in the table, and have not conceded a goal in any of their last five matches, although goals have been hard to come by with only three scored.
There will be a minute's silence and the French national anthem will be played before every Premier League match this weekend, which Van Gaal says shows support to the French people.
English also fans joined in singing La Marseillaise at Wembley on Tuesday and Van Gaal said: "We, as a member of the sport of football, cannot do too much -- we can give support in symbols and this is a nice thing for the French people, the victims, their relatives to give them force and strength to survive."
(Reporting by Mike Collett; Editing by John O'Brien)
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