In instructions for keeping the Day of Atonement, Leviticus 23:32 1 states:
It shall be to you a Sabbath of solemn rest, and you shall afflict yourselves. On the ninth day of the month beginning at evening, from evening to evening shall you keep your Sabbath.” (ESV)
It will be a Sabbath of complete rest for you, and you must practice self-denial. You are to observe your Sabbath from the evening of the ninth day of the month until the following evening. (CSB)
Most translations state this requirement in general terms like "afflict yourselves" or "self denial."
Some specifically call out fasting:
This is a time of complete rest just like the Sabbath, and everyone must go without eating from the evening of the ninth to the evening of the tenth. (CEV)
It shall be to you a sabbath of rest, and you shall afflict yourselves [by fasting in penitence and humility]. On the ninth day of the month from evening to evening you shall keep your sabbath (AMPC)
Fasting seems to be both a logical and necessary component of "self denial" and eating would seem contrary to the requirement and a violation of the instructions.
Is fasting required on the Day of Atonement?
1. A similar instruction is given in Leviticus 16:31