The 31-year-old midfielder suffered cartilage and tendon damage in his ankle during the 4-2 defeat to Eintracht Braunschweig on February 15.
The Holland international was forced off the pitch early in the second half at the Eintracht-Stadion after he went over on the ankle following a collision.
Following scans, club captain Van der Vaart was expected to be sidelined for three weeks, but said he could return in time for the 100th Northern derby against Werder on Saturday after completing training on Tuesday with no adverse reaction.
He told www.kicker.de: "If I can train all week well, I'm fit for Bremen."
Meanwhile, defender Heiko Westermann is suffering from flu and striker Pierre-Michel Lasogga should rejoin the rest of the squad for training on Wednesday following a sprain.
But Czech Republic goalkeeper Jaroslav Drobny sustained a calf muscle injury during the warm-up for Saturday's 3-0 victory over Borussia Dortmund and is likely to be sidelined against Werder.