CAIRO — The Egyptian authorities have arrested a 19-year-old British tourist over a video he filmed on his cellphone that showed a military helicopter in the background, his family said.

The teenager, Muhammed Fathi Abulkasem, who is Libyan and British, was arrested shortly after he arrived in the Egyptian coastal city of Alexandria on Nov. 21 from neighboring Libya, his cousin Shareen Nawaz said on Friday.

Egypt’s Foreign Ministry could not immediately be reached for comment. Britain’s Foreign Office confirmed the arrest of a Briton in Alexandria to Reuters, but did not elaborate. His mother, Amaal Rafiq, confirmed his arrest in a Facebook post.

“We didn’t hear from him until 12 hours later,” Ms. Nawaz said. “He basically told us he is held on suspicion of collecting information against the military.”