Wood, 31, has just rejoined England on the tour of India after being rested for the first two Tests of the series.
If he had been selected by one of the eight IPL teams, he could potentially have been away from home until June.
Sixteen English players will be in the auction, while another eight have been retained by their franchises.
Wood’s decision comes in the midst of scrutiny of England’s policy of resting players during their winter tours to Sri Lanka and India.
All the other players who have so far spent time away from the Test side – Ben Stokes, Jofra Archer, Jos Buttler, Sam Curran and Jonny Bairstow – played in the previous edition of the IPL in the autumn and will again feature in the next tournament, which runs from April to June.
Moeen Ali, who will be rested for the final two Tests in India, is due to be in the auction.
On Wednesday, coach Chris Silverwood apologised for the manner in which Moeen’s departure from the India tour was confirmed.
England captain Joe Root initially said Moeen had “chosen” to go home, whereas his period of rest had actually been planned beforehand.
His decision to miss this year’s IPL means Wood, who has a young son, will be available for England’s home Test series against New Zealand in June.
Some England players could miss the two Tests if their IPL teams reach the latter stages of the tournament. (Courtesy BBC)