"At least 20 suspected ADF collaborators have been arrested, to assist with our investigations," the country's police force said in a statement.
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In November, the group, which controls swathes of the country, attacked another hotel in Mogadishu, killing nine people.
The attack on the popular upmarket Pearl Restaurant, on the capital's Lido Beach, happened early on Friday evening.
A team from the ministry and other authorities was able to capture the shark, adding that local authorities had issued a ban on several beaches near the attack site.
BFM TV reported that the attack had happened in a park and that the assailant had been a Syrian asylum seeker.
Prime Minister Benjamin Netanyahu said that the incident was serious and unusual and promised that it would be thoroughly investigated.
A group of people, including hotel staff, attacked the protestors, violently pushing them and throwing chairs at them.
The Foreign Ministry said in a statement that it is in contact with Aviel's family in Israel and is helping them during these "difficult times."
Police arrived at the scene and shot the assailant twice.