The 32-year-old will undergo X-rays after landing awkwardly following an aerial challenge during his side's 4-0 win over Guiseley.
"Unfortunately it looks like he has broken his arm. We won't know for certain until we get the X-rays but it does look that way," Bradford manager Phil Parkinson told reporters.
"It is a blow for Andy because he has come back looking really fit. He has worked hard on his fitness over the summer and he has been towards the front with all the running tests.
"He has shown a great attitude in training so far, so it is a blow. These things do happen, however, and we'll get him back as soon as we can."
The injury will rule Gray out of the Bantams' tour of Ireland next week.