Dike tore his anterior cruciate ligament in a friendly game against Seattle Sounders last week and has consequently been ruled out until August at least.
Timbers have now listed Deon McCaulay, a Belizean international forward as a possible replacement for Dike, who underwent successful surgery last weekend.
Lamenting the loss of the Nigerian striker, Timbers head coach Caleb Porter said: "It’s too bad. We feel for Bright. He was going to be a key piece for us this year. But that’s football, it happens and guys get injured.
"He’s a tough kid, he’s a great kid, he’s a good kid. We’ll miss him, but he’ll overcome this.”
The 26-year-old, who scored five goals in Timbers’ final 11 games of last season, made his international debut for Nigeria in a friendly game against Venezuela last November and was part of coach Stephen Keshi's 32-man provisional squad for the Nations Cup, until he was left out of the final 23-man roster.