Williams, 18, was to have made her debut in the 16-player season finale as the fourth seed against Dominique Van Roost of Belgium.
"This was the first year I've qualified for the Chase and I can't believe this had to happen," Williams said in a statement.
She was immediately replaced in the singles draw by the 19th-ranked Russian Elena Likhovtseva. The doubles team of Serena and sister Venus Williams will be replaced by Conchita Martinez of Spain and Argentina's Patricia Tarabini, the WTA Tour said.
Williams is the second big name to withdraw. Last week, injured three- time champion Monica Seles was forced to pull out of the tournament that is already missing recently retired former champions Steffi Graf and Jana Novotna.
The fourth-ranked Williams, who was looking to cap a sensational breakthrough year at the Chase, said she was about 40 minutes into an early morning workout when the injury occurred. "After a few forehand volleys I suddenly felt an excruciating pain in the upper left side of my back," Williams said. "I couldn't move, run, walk and even the simplest task of breathing became nearly impossible."
Stroia said a doctor diagnosed the injury as a "vertebral dysfunction" and prescribed anti-inflammatory medication and a series of treatments, including electrical stimulation, massage and strengthening exercises.
Mary Pierce, the fifth seed, held off Anna Kournikova on Monday's opening night.
Pierce was on her way to becoming the tournament's first victim of an upset before she engineered a remarkable comeback, helped by a near total collapse by the Russian teenager, to produce a 6-7, 7-6, 6-0 victory in just over two hours on the blue carpet at Madison Square Garden.
At the site of many great title fights of the past, Kournikova had Pierce on the ropes in the second set but could not deliver a knockout blow. The 18-year-old Kournikova appeared to be in complete control in the second set with Pierce barely hanging on.
Twice in the sixth game Kournikova was a point away from seizing a 5- 1 lead that would have left her serving for the match, but Pierce saved both break points to progress to 4-2. "I just said to myself, `anything can happen. Just play every point the best you can'," Pierce said.
The seventh-seeded Barbara Schett made the most of her Chase Championships debut by beating Spain's Arantxa Sanchez-Vicario 6-1, 6-4. It was the Austrian's third win over the declining Sanchez-Vicario in as many meetings this year.
"It's just great to be here, great to play here in Madison Square Garden," she said.
Results, Digest, page 31