The 66-year-old coach has seen his side, who looked unstoppable early in the season as they clocked up 10 wins in a row without conceding a goal, drop to third in the Bundesliga, four points behind leaders Borussia Dortmund.
Bayern's slump has coincided with injuries to Schweinsteiger who suffered a dislocated shoulder against Napoli in November, then suffered an ankle injury this month only four matches into his comeback.
On Saturday, Bayern were devoid of creativity as they drew 0-0 at lowly Freiburg in the Bundesliga.
"For me, Bastian Schweinsteiger plays in the same league as Xavi, as Iniesta and Sergio Busquets," Heynckes told reporters, referring to the three superb Barcelona midfielders.
"He's a strategist, he's the brains of the team and it's not been so easy without him in the last games."
Schweinsteiger rescued Bayern on their last visit to Basel, scoring twice as they came from behind to win 2-1 in a group game in last season's competition. He also scored twice for Germany at St Jakob-Park during Euro 2008.
Heynckes accepted criticism of Bayern's recent performances which have also included a 3-1 defeat by Borussia Moenchengladbach who are now second in the Bundesliga.
"The criticism is justified and we have to respect it," said Heynckes. "But I'm convinced that on Wednesday we can produce a good performance."
"We haven't yet played convincingly in 2012," said striker Mario Gomez. "We must not underestimate Basel, they are a very strong team with their fans behind them, although we have enough quality to get to the next round."