The move affects broadcasts in the capital Dushanbe and the northern city of Khujand. The BBC's services on medium and short wave are unaffected, RFE/RL's Tajik Service reports.
The decision to suspend the service was made on 10 January and follows the adoption of a law requiring foreign media outlets with FM services to register with the Justice Ministry.
The BBC said the 20-day registration deadline had been "unrealistic" because the process normally took up to six months to complete.
Britain's envoy to Tajikistan, Graeme Loten, said in a statement that the embassy had expressed its concern to the Tajik Foreign Ministry. He called the suspension a "misunderstanding."
A Foreign Ministry spokesman, Igor Sattarov, told reporters that his ministry was working with the Justice Ministry and the BBC to resolve what he called a "procedural question."
(RFE/RL's Tajik Service)