Kwiatkowski came down on the dusty descent of the Alto de Ceal with Sky team mates Sergio Henao and Tao Geoghegan Hart.
The Polish rider never made it back to the main bunch, despite he and Henao's best efforts, crossing the line 25 seconds behind the main general classification bunch.
“The guys were in a super position and took it easy and careful in the descent," Sky director Gabriel Rasch said. "Despite that Tao, Sergio and Kwiato all slipped on the same corner at the same time.
"Kwiato had to change his bike but luckily the guys were just behind and gave him a bike quickly. Sergio did an amazing job after that and they almost managed to close the gap to the group ahead. It could have been worse."
As a result, Kwiatkowski surrendered his second position overall - and the points jersey - to Alejandro Valverde who finished third on the stage.
“It was a difficult stage to handle," Valverde said. "I took two seconds of bonus in the sprint and four more at the finish so it’s a good day.
"We want to keep going like that. They told me it was a hard finish but it was even harder than I expected.”
Sky co-leader David De La Cruz managed to avoid the crash and finished with Valverde and the GC favourites.
“David was in the first group and he was comfortable there. He tried to slow it down a bit and just follow the big names," Rasch explained. "It was good to have him up there.”
How the GC looks now after Stage 7
Besides Kwiatkowski's time loss, the general classification remains largely unchanged although Tony Gallopin's victory earned him an improvement in the overall standings as did Valverde's third place on the stage.
1. Rudy Molard (Groupama-FDJ)
2. Alejandro Valverde (Movistar) +47
3. Emanuel Buchmann (Bora-hansgrohe) +48
4. Simon Yates (Mitchelton-Scott) +51
5. Tony Gallopin (AG2R Mondiale) +59
6. Michal Kwiatkowski (Sky) + 1:06
7. Ion Izagirre (Bahrain Merida) +1.11
8. Nairo Quintana (Movistar) +1.14
9. Steven Kruijswijk (LottoNL Jumbo) +1.18
10. Enric Mas (Quick-Step Floors) +1.23
11. George Bennett (LottoNL Jumbo) +1.26
12. Miguel Angel Lopez (Astana) +1.27
13. Fabio Aru (UAE) +1.28
14. Rigoberto Uran (EF Drapac) +1.29
15. David De La Cruz (Sky) +1.34