File photo showing A video grab from Algeria 3 public channel shows Algerian President Abdelmadjid Tebboune giving a televised speech, on February 18, 2021 in Algiers. AFP
Algeria in an official note "firmly protested against the clandestine and illegal exfiltration of an Algerian citizen" via Tunisia to France, a statement from the presidency said, adding that Tebboune had ordered ambassador Said Moussi to be recalled "with immediate effect".
Bouraoui, 46, had been arrested in Tunisia on Friday and risked being deported to Algeria, but she was finally able to board a flight to France on Monday evening.
The French-Algerian doctor by training, who is also a journalist and activist, was sentenced in Algeria in May 2021 to two years in jail for "offending Islam" and for insulting the president.
She has not been placed under arrest since then pending an appeal.
Bouraoui was subject to a ban on leaving Algeria, and was arrested in Tunisia when trying to board a flight for France.
A judge released her on Monday but she was then taken away by police before obtaining protection from the French consulate in Tunis.
Shortly before Moussi was recalled on Wednesday, the Algerian foreign ministry said it had sent an official note to the French embassy expressing "the firm condemnation by Algeria of the violation of national sovereignty by diplomatic, consular and security personnel of the French State".
It said these French personnel in Tunisia "engaged in a clandestine and illegal operation to exfiltrate an Algerian national".
In the note, Algeria said the incident had caused "great damage" to Algerian-French relations.
Ties between the two countries had been frosty since autumn 2021, but warmed when French President Emmanuel Macron visited Algiers last August.
French Prime Minister Elisabeth Borne led a delegation of 15 ministers to the North African country last October to bolster that reconciliation.