At least 29 people were killed in the siege on a luxury hotel in the capital Ouagadougou, and more than 126 were taken hostage.
The FCO said the attack had now come to an end, but warned that further incidents were possible.
It also said that it had not been advised as to whether the curfew, which was put in place following the attack, had yet been lifted.
It warned that airports and borders “could be subject to closure at short notice”.
The FCO added: “If you are in Burkina Faso you should exercise caution and follow the instructions of the security authorities, avoiding the area around the Splendid and Yibi Hotels and respecting any curfew”.
FCO issues advice in wake of Burkina Faso terror attack
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