The 31-year-old had been at the centre of a transfer saga on deadline day over a protracted move to Queens Park Rangers.
Odemwingie had driven himself to Loftus Road in the belief that he was on the verge of a move away from The Hawthorns, but a deal was never agreed between the two clubs.
After accepting his punishment, Odemwingie released a statement saying: "I understand how my actions have been viewed and I want to apologise to the club and the supporters for any distress that I have caused.
"I want to reassure everyone at the club and the fans that I will continue to give my all whenever I am selected.
"We have enjoyed a good season so far and I aim to play my part in keeping the club as high up the table as possible."
Odemwingie is now available for selection and he could return to the Baggies squad for their match with Liverpool on Monday night.