All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
A vow requires a wording that implies a commitment to do a specific act of obedience; Ibn Qudaamah wrote, "The wording of a vow is to say, 'It is due upon me to Allaah to do such-and such.' If the person says, 'I vow to do such-and-such,' then it is also binding because he explicitly said the term 'vow'. It is also considered a vow when he says, 'If Allaah cures me (of my illness), I will fast a month.'" [Al-Mughni]
Hence, the wording mentioned in the question is not considered a vow; it is a mere promise. The sayer should keep his promise; however, he is not obliged to do so. For more benefit, please refer to fatwa 86010.
Allaah knows best.