Club officials were "furious" with the former Real Madrid star's behaviour but there is no chance of him ending his contract this month despite speculation linking him with European clubs, the source added.
Benzema left for holidays during the Saudi Pro League's mid-season break three weeks ago and shut down his Instagram account, which is followed by 76 million users.
A different source said Benzema, who won the Ballon d'Or in 2022 and is reportedly being paid 100 million euros (£85.8 million) a season, had been on holiday in Mauritius until Monday.
"Benzema arrived Thursday evening, 17 days late. He should have returned on January 2nd," the source close to the club said.
"We couldn't reach him for 10 days. The club management and the coach are furious with what happened.
"There will be a meeting with the club board to explain what happened and discuss his future."
The source said Benzema remains captain of Al Ittihad and there was "no option" for him to leave the club. Some reports have linked him with a move to Premier League side Chelsea.
Benzema was one of the biggest names to move to the Saudi league last year, along with Cristiano Ronaldo, former African Footballer of the Year Sadio Mane, Brazilian superstar Neymar and a host of other players from Europe's top leagues.
One of the high-profile signings, former Liverpool captain Jordan Henderson, quit his Saudi club AlEttifaq on Thursday after playing just 19 games and joined Dutch side Ajax.
Benzema's club, one of four in the league owned by the Saudi Public Investment Fund, slipped to seventh in the table in December after three consecutive defeats, leading to Benzema being booed by supporters.
The Saudi league resumes on February 7th.
