Djokovic was given a bye in his first round in Barcelona, while Klizan came through two qualifying rounds and a tight first-round match against Federico Delbonis.
Twelve-time grand slam victor Djokovic was a late addition to the draw following his third-round exit in Monte Carlo last week, but his stay in Catalunya proved even shorter. The Spaniard will now face Martin Klizan or Novak Djokovic in the next round.
Djokovic, who has struggled in his return from a right elbow injury, also lost in the second round in Miami and Indian Wells this season.
The 28-year-old Klizan, who reached a career-high rating of 24 in 2015, took the primary set in spectacular vogue, a mix of aggression and a deft contact proving too good for his opponent. "I will try to continue and see where it takes me". This was the first time I played him on clay and I beat him and it feels great. "It's a great feeling, it's just fantastic".More news: Buhari Vows Punishment For Benue Church Attackers
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"It was a hard game and I committed a couple of errors at the start".
Nishikori had lost to Nadal in the Monte Carlo Masters final on Sunday and he pulled out after conceding the first set to Garcia-Lopez 6-3.
Second-seeded Bulgarian Grigor Dimitrov, from Bulgaria, eliminated France's Gilles Simon 6-2, 6-1, while Austria's Dominic Thiem saw off Spain's Jaume Munar 7-6 (10-8) 6-1.
The Japanese missed last year's U.S. Open and the Australian Open at the start of 2018 after injuring the same wrist in August.