American Woods, 40, has not played tournament golf in almost a year and had two operations last autumn in an attempt to cure a back problem.
His agent has confirmed he will not play for the rest of this season as he is not ready for "competitive golf".
The 14-time major winner has dropped to a world ranking of 628.
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Kvitova, who was playing only her third tournament of 2017 after being stabbed by an intruder at her home in December, lost 6-1 1-6 6-2 on court two.
The American had never won a singles game at Wimbledon before this year and is ranked 95th in the world.
In the deciding set, Kvitova struggled physically and needed medical help, but managed to complete the match.
"I'm glad it is over," said the 27-year-old Czech player afterwards.
"It was really tough and I feel really empty. My body is not great but mentally I'm glad it is over.
"I just need to look to the future and focus and prepare for the next tournament."
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Elsewhere, Venus Williams lost the first set before beating world number 55 Wang Qiang 4-6 6-4 6-1 to move into the last 32.
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Five-time Wimbledon champion Williams, 37, was 4-2 ahead in the opening set, but lost four consecutive games to lose the first set, but recovered to move into the third round.
She broke Wang's serve late in the second set and twice more in the deciding set for the victory.
Williams, who last won the Wimbledon title nine years ago, will play unseeded Japanese player Naomi Osaka in the last 32 after she defeated 22nd seed Barbora Strycova of the Czech Republic 1-6 6-0 6-4.
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Former world number one Victoria Azarenka reached the third round with a 6-3 6-3 win over 15th seed Elena Vesnina.
Azarenka, 27, is playing only her second tournament of 2017 after giving birth to her son Leo in December.
The Belarusian, ranked 683rd, broke the Russian's serve in the sixth game on her way to taking the opening set.
Azarenka broke Vesnina's serve twice more in the second set to secure a match with Britain's Heather Watson.
Vesnina, a Wimbledon semi-finalist in 2016, needed medical attention in the second set as she was struggling with a hip injury, but was able to complete the match.
World number 86 Camila Giorgi of Italy secured a big upset as she knocked out American 17th seed Madison Keys 6-4 6-7 (10-12) 6-1.
Giorgi served for the match in the second set but was broken and then wasted four match points, including one on her own serve, in an epic tie-break.
Ultimately, it did not matter as Giorgi stormed through the deciding set to move into the third round of Wimbledon for the fourth time in her career.
Women's second seed Simona Halep is safely into the last 32 after a straight-set win over 21-year-old Brazilian Beatriz Haddad Maia.
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Halep won it 7-5 6-3 to set up a third-round tie with China's Shuai Peng, a 6-2 6-2 winner over Spanish 25th seed Carla Suarez Navarro.
Eighth seed Dominika Cibulkova, of Slovakia, who reached the last eight last year, also moved into the third round. The Slovak defeated unseeded American Jennifer Brady 6-4 6-4 on court 18.
It was a routine day for fourth seed Elina Svitolina of Ukraine, who cruised past unseeded Italian Francesca Schiavone 6-3 6-0.
French Open champion Jelena Ostapenko had to fight hard to get past unseeded Francoise Abanda of Canada.
Ostapenko, the 13th seed from Latvia, lost the first set 6-4, but took the next two 7-6 (7-4) 6-3 to advance.
Tiger Woods has withdrawn from the US PGA, meaning he will miss all four majors in a calendar year for the first time since his Masters debut in 1995.
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Two-time Wimbledon champion Petra Kvitova was beaten in the second round by American Madison Brengle.