The tweet said: "If you are resident in Christchurch East don't forget to vote today - for Labour and Poto Williams."
Mr Cunliffe has 6464 followers on Twitter who would have received the tweet.
In a statement the Electoral Commission said it believed the statement constituted a breach of section 197 (1)(g)(i) of the Electoral Act because it was a statement published on polling day" advising, or intended, or likely to influence electors as to the candidate for whom they should or should not vote in the byelection."
Mr Cunliffe said yesterday he had removed the tweet on Saturday as soon as the mistake was pointed out to him.
Poto Williams won the seat convincingly.
Mr Cunliffe said in a statement: "I understand this is a routine part of the Commission's process. I will be co-operating fully with any inquiry and won't be making any further statement on this matter as it is now part of a formal process."
