The world No. 1 Djokovic outlasted Belgian Xavier Malisse 6-2, 4-6, 7-5 in 2 hours, 13 minutes at St. Jakobshalle. The U.S. Open, Wimbledon and Australian Open champion Djokovic, now 65-3 for the year, had been sidelined since September due to a back injury.
Djokovic was last year's Basel runner-up to hometown hero Roger Federer and beat Federer in the 2009 finale here.
The fifth-seeded Fish, meanwhile, won the first game of his opening-round match against qualifier and fellow American James Blake before he quit due to a left hamstring injury.
Fish is hoping to qualify for the season-ending ATP World Tour Finals for the first time. He is currently in the eighth and final spot for the exclusive event, which will start November 20 in London.
Other Tuesday winners were Finn Jarkko Nieminen, Swiss Stanislas Wawrinka and qualifier Michael Lammer, Croat Ivan Ljubicic, and Italian Andreas Seppi. Wawrinka defeated Croat Ivan Dodig 6-4, 6-4, while Nieminen, who was the Basel runner-up to the Swiss icon Federer in 2007, outlasted Brazil's Thomaz Bellucci 6-7 (5-7), 6-4, 6-3. The veteran Nieminen will battle a third-seeded Federer in a second-rounder on Wednesday. The 16-time Grand Slam champion Federer has won four of the last five championships in his native Basel. Lammer got his first ATP-level win of the year by besting Russian Mikhail Youzhny 6-4, 6-3.
In some opening-round action here on Wednesday, second-seeded Aussie Open runner-up Andy Murray will meet Dutchman Robin Haase and seventh-seeded former world No. 1 Andy Roddick will encounter oft-injured former world No. 2 Tommy Haas. The red-hot Murray has won his last three tournaments and is riding a 13-match overall winning streak.
The 2011 Basel champion will collect $450,000.