The Romanian will miss out on the matches against Seattle Sounders, Toronto and Chicago Fire later this month after suffering stiffness in his lower back.
Chiriches joins Sandro in being absent for the pre-season fixtures.
The Brazilian midfielder has been suffering with a virus and will remain in England.
"Vlad has been complaining of stiffness in his lower back and is continuing to be assessed to determine the extent of the problem," read a statement on Spurs' official website.
"Sandro is recovering from a virus and has been kept behind on medical advice to avoid the risk of spreading the infection."
Meanwhile, Spurs midfielder Alex Pritchard has signed a new deal keeping him under contract at White Hart Lane until 2016.
The 21-year-old has joined Championship newcomers Brentford on loan until the end of the season.
