Surrey Police branded the two youths aged 14 and 16 "dangerous and irresponsible" following the blaze at the Peacocks Shopping Centre, Woking.
Sgt Andy Audsley said a number of people would have been in the complex at the time and the fire might have spread and put them at risk.
He appealed for witnesses to the incident on Sunday to contact police.
The blaze caused about a £100 worth of fire and smoke damage to the entrance of the complex.
The teenagers are described as being white, with dark scruffy hair. They were both wearing black jogging bottoms, white trainers and black hooded tops.
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