Silvestre, 30, was stretchered off just before half-time in Saturday's 1-0 win at Everton after collapsing in pain.
It is the latest in a series of knee injuries to hit the Old Trafford camp.
Park Ji-Sung and England keeper Ben Foster are both at different stages of recovery from cruciate ligament surgery, while Ole Gunnar Solskjaer announced his retirement this month after failing to recover from a long-term knee complaint.
John O'Shea is also out after sustaining an injury on Republic of Ireland duty last week, while youngsters Gerard Pique and Johnny Evans are likely to be among Ferguson's squad when United open their Champions League campaign against Sporting Lisbon in Portugal on Wednesday.