PSV Eindhoven's Wijnaldum has an ankle injury and left the Dutch training camp earlier on Monday.
Netherlands visit Estonia on Friday and Andorra four days later and two wins would guarantee top spot in Group D and automatic qualification for next year's World Cup in Brazil.
The 29-year-old Sneijder, who has 93 caps, returns after losing the captaincy for two internationals in Asia in June and also being passed over for last month's friendly in Portugal.
Sneijder's omission from the squad sparked controversy in the Dutch media with coach Louis van Gaal explaining he did not feel the Galatasaray player was fit enough.
When he left him out of his 21-man squad for the qualifiers on Friday, van Gaal said Sneijder was on his way back to form but needed up to seven more weeks to get properly fit and could best use the international break to work on his fitness.