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A severe hailstorm hit as the riders scaled the Col de Mont-Louis with 15km (9.32 miles) remaining of the 174km ride from Gruissan to Font-Romeu.
Overall race leader and favourite Tadej Pogacar was seen indicating to the main group to pull off the course and soon afterwards drenched riders took shelter in a nearby hotel.
Shortly afterwards organisers announced the stage would not resume and there would be no winner or podium ceremony.
Conditions had been warm and sunny on the flat approach to the mountainous finish with a five-man breakaway group out in front.
Slovenian Pogacar, aiming to complete his Grand Tour collection by winning the Vuelta for the first time, was always near the front of the pack.
Pogacar won the opening stage time trial on Saturday, before Britain's Matt Brennan sprinted to victory in the second stage on Sunday.
Tuesday's fourth stage - the first mountain stage of the tour - is a 104.8km route that starts and finishes in Andorran capital Andorra la Vella.
Vuelta a Espana general classification after stage three abandoned
Tadej Pogacar (Slo/UAE Team Emirates-XRG) 4 hours 58mins 40secs
Wout van Aert (Bel/Team Visma-Lease a Bike) +9secs
James Brennan (GB/Team Visma-Lease a Bike) +10secs
Leo Bisiaux (Fra/Decathlon-CMA CGM) +12secs
Finn Fisher-Black (NZ/Red Bull-Bora-Hansgrohe) +14secs
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