Fletcher, 24, is Boro’s top scorer with 10 goals in all competitions this season and has regularly led the line on his own.
After a frustrating start to the campaign, Fletcher’s stats improved in December and January as the forward netted six goals over an 11-game period.
Yet goals have dried up for Boro and Fletcher, and the Teessiders have now gone three games without scoring.
Woodgate does have options up front following Britt Assombalonga’s recovery from an ankle injury and Lukas Nmecha’s loan arrival from Manchester City.
Yet the Boro boss hasn’t been able to find the right combination in recent weeks, with his side struggling to create changes against Luton, Barnsley and Leeds.
When asked about Fletcher ahead of Monday’s meeting with Nottingham Forest, Woodgate said: "If you look at his career he hasn’t scored goals constantly, week in week out. He has moments when he scores and moments when he doesn’t score.
"I need Britt to step up to the mark, I need Lukas to step up to the mark to score goals. I still believe in my forwards."
Fletcher and defender George Friend were both forced off with hamstring injuries during Wednesday’s defeat to Leeds.
Woodgate is hopeful the setbacks won’t be long-term, though, and didn’t rule either player out of the Forest clash.