A growing list of organizations and individuals that have tangled with WikiLeaks and its detained founder, Julian Assange, have suffered online attacks, in what appears to be an effort by hackers bent on exacting revenge for the document-leaking website.

The attacks stepped up Wednesday, a day after Mr. Assange was arrested and denied bail in London in connection with sexual-misconduct accusations in Sweden. A range of organizations, including MasterCard Inc., Visa Inc., and the Swedish prosecutor's office, reported technical...