Bamford returned to training this week upon his recovery from a ruptured plantar fascia and Marsch was optimistic that the Whites no 9 might be able to feature in the crucial season finale against the Bees.
The Whites boss was mindful of not putting Bamford at risk and was set for one last meeting with the striker to assess his condition on the eve of the clash at Brentford.
Marsch, though, has now revealed that the striker has Covid-19, telling Sky Sports: "With Patrick, he was fit and ready to go and two days ago he tested positive for Covid and he has been really sick and unable to get out of bed."
The one change to the Leeds team sees young forward Greenwood handed a first Premier League start as Mateusz Klich drops to the bench which also features a fit again Tyler Roberts.
Roberts returned to training after successful surgery on a ruptured hamstring and recovery this week but Marsch said at his pre-match press conference that today's game would come too soon.
In addition to Bamford, Leeds have six players out as Dan James is suspended whilst Luke Ayling (knee), Adam Forshaw (fractured kneecap), Stuart Dallas (femoral fracture) and Crysencio Summerville (twisted knee) are out injured.
Third-bottom Leeds and fourth-bottom Burnley are level on points but the Whites have a far inferior goal difference which means United will go down if the Clarets beat Newcastle United at Turf Moor.
Should Burnley lose or draw, Leeds will be safe if producing a better result at Brentford.
Brentford boss Thomas Frank has made one change to his side as Vitaly Janelt replaces the injured Christian Norgaard.
Former Whites defender Pontus Jansson captains the Bees whilst Frank Onyeka returns from injury to sit on the bench.
Brentford: Raya; Ajer, Jansson, Bech, Henry; Janelt, Jensen, Eriksen; Mbeumo, Wissa, Toney. Subs: Fernández, Canós, Dasilva, Onyeka, Jeanvier, Baptiste, Roerslev, Stevens, Young-Coombes
Leeds United: Meslier, Firpo, Koch, Cooper, Llorente, Phillips, Harrison, Rodrigo, Raphinha, Greenwood, Gelhardt. Subs: Klaesson, Struijk, Hjelde, Cresswell, Shackleton, Bate, Klich, Gray, Roberts.