A hadeeth concerning this was narrated from the Prophet (peace and blessings of Allaah be upon him) but it is da’eef (weak).
In al-Jaami’ al-Sagheer, al-Suyooti attributed it to Ibn Shaheen in his Targheeb: It was narrated from al-Diya’ from Jareer ibn ‘Abd-Allaah (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “The month of Ramadaan is suspended between heaven and earth and is not taken up to Allaah except by zakaat al-fitr.”
It was classed as da’eef by al-Suyooti. Al-Mannaawi explained the reason for that in Fayd al-Qadeer, where he said: It was narrated by Ibn al-Jawzi in al-Waahiyaat and he said: it is not saheeh; its isnaad includes Muhammad ibn ‘Ubayd al-Basri who is majhool (unknown).
It was also classed as da’eef by al-Albaani in Silsilat al-Ahaadeeth al-Da’eefah (43). He said: Even if the hadeeth were saheeh, the apparent meaning is that acceptance of the Ramadaan fast is dependent upon payment of sadaqat al-fitr, and if a person does not pay it, his fast will not be accepted, but I do not know of any scholar who says that … and the hadeeth is not saheeh. End quote.
As the hadeeth is not saheeh, no one can say that the fast of Ramadaan is only accepted with zakaat al-fitr, because no one can know that except the Prophet (peace and blessings of Allaah be upon him).
It is proven in Sunan Abi Dawood that Ibn ‘Abbaas (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) enjoined zakaat al-fitr as a purification for the fasting person from idle speech and obscene talk, and to feed the poor.” Classed as hasan by al-Albaani in Saheeh Sunan Abi Dawood.
This hadeeth explains the wisdom behind zakaat al-fitr, which is to make up for any shortfall that occurred during fasting. It does not say that fasting will not be accepted without zakaat al-fitr.
And Allaah knows best.