Coach Louis van Gaal has replaced the Galatasaray midfielder in his squad with AZ Alkmaar's Adam Maher, 19.
Sneijder, playing his first international since September, was forced off in the first half of Friday's 3-0 victory over group rivals Estonia in Amsterdam.
Rafael van der Vaart, who went on in his place, opened the scoring in the 46th minute before Robin van Persie and Ruben Schaken sealed the win.
"I pulled my groin muscle. It won't keep me sidelined for long but Tuesday's game comes too early," Sneijder told reporters.
The Dutch are top with 15 points after winning all five matches. Romania, in third, and second-placed Hungary are five points adrift.