Hilal winger Shalhoub was ruled out after picking up an ankle injury in a warm-up game against North Korea this week, while Ittihad Jeddah defender Montashari was dropped for technical reasons.
Dos Anjos also axed the team's qualifying top scorer Saleh Beshir and midfielder Saheb Al-Abdullah, but it was Montashari's omission that created a lot of question marks around the Portuguese manager.
"You have to ask the manager, I am fit and ready to play," replied Montashari to Al-Watan newspaper when asked about his omission.
Montashari was voted Asian Player of the Year in 2005, as he guided Ittihad to the Saudi League triumph this last season, when he scored a last-gasp winner against Hilal in the final.
Saudi Arabia face a crunch start to their Asian Cup campaign, when they meet South Korea on Wednesday in Group D.