Ali Rehmat Assadi will stand trial in the UAE on charges of abducting Abbas Yazdi, who went missing in June, the source added. Mr Yazdi's wife, Atena, has told UAE media she feared he might have been kidnapped by Iranian intelligence officers.
Iran has denied any role in Mr Yazdi's disappearance.
UAE authorities said in January they had detained three Iranians suspected of being part of a group that had kidnapped Mr Yazdi, a businessman who owns a general trading company in the Gulf Arab emirate.
The official source said on Sunday that Mr Assadi, the subject of an Interpol "red notice" or international wanted persons alert requested by Dubai, was the fourth principal member of the group. There was no immediate word on why Mr Assadi had been in Thailand.
The Iranian and British governments had been informed of Mr Assadi's arrest in line with diplomatic and consular regulations, the source said.
Britain's Foreign Office said in August it was in touch with the Dubai and Iranian governments over the case of Mr Yazdi, who was 44 years old at the time of his disappearance.
UAE newspaper 7Days has cited Mr Yazdi's wife as saying the trader and investor was a close childhood friend of the son of former Iranian President Akbar Hashemi Rafsanjani.
Britain is among Western nations at odds with Iran over its nuclear programme and other issues. It shut its embassy in Tehran after what it called "an attack by government-sponsored militias" on the mission in November 2011. Iran's embassy in London was also closed.
British media had reported that, at the time of his disappearance, Mr Yazdi was giving evidence by video link to an international arbitration tribunal in The Hague intended to settle a long-running commercial dispute involving United Arab Emirates-based Crescent Petroleum and the National Iranian Oil Company.
There is no suggestion that this involvement in the arbitration is connected to his disappearance, British media have said.