Also exiting the French Open at the first hurdle was four-time grand slam winner Naomi Osaka, an unhappy return a year after pulling out of the claycourt tournament to protect her mental health.
Iga Swiatek, the world No.1 and favourite, has progressed, along with former grand slam champs Petra Kvitova, Victoria Azarenka, Emma Raducanu and Bianca Andreescu.
Krejcikova's defeat is not so much a shock as it sounds as this was her first match in three months because of an injured right elbow.
Nevertheless, she started sharply winning eight of the first nine games to take a one-set lead only for Parry, 19, to reel off six straight games to tie the match before winning 1-6 6-2 6-3.
Parry received raucous backing from spectators shouting for her at Court Philippe Chatrier, where the noise echoed under the retractable roof pulled shut because of rain.
"It's a dream for me. It was always a dream to play on this court, with the French crowd to support me. They clearly pushed me to victory today," Parry said. "I'm the happiest person right now."
Krejcikova, in contrast, was in tears as she described how she 'hit a wall'.
She added: "I just collapsed physically. It was tough because I didn't play the matches. Matches are different to practices. I tried to prepare the best way I could."
However, she added she was 'happy' just to have made it to Paris as at one stage she thought her elbow injury would prevent her competing at all.
The only other women to lose in the first round when defending the French crown were Anastasia Myskina in 2005 and Jelena Ostapenko in 2018.
Osaka lost 7-5, 6-4 to Amanda Anisimova, a 20-year-old American who beat the Japanese in the third round at the Australian Open in January.
Osaka double-faulted twice on break point, to go 5-6 down in the first set and 3-4 down in the second. Each time Anisimova made the break count.
Top seed Swiatek, the 2020 champion, extended her winning streak to 29 matches beating Ukraine's Lesia Tsurenko 6-2 6-0 in 54 minutes.
Swiatek's winning streak is the longest by any woman since Serena Williams won 34 in a row in 2013.
She has won the title at her past five tournaments and has also won a tour-leading 14 sets by 6-0 this season.
Kvitova, a two-time semi-finalist in Paris, beat Anna Bondar 7-6 (7-0) 6-1 while Azarenka, a semi-finalist in 2013, defeated Ana Bogdan 6-7 (7-9) 7-6 (7-1) 6-2.
Briton Emma Raducanu won on her Roland Garros debut but was made to work for her victory as she came back from a set down to beat Czech qualifier Linda Noskova 6-7(4) 7-5 6-1.
Andreescu found her rhythm after a slow start to defeat Belgium's Ysaline Bonaventure 3-6 7-5 6-0.
With agencies
6°C