The former Fulham ace returned to action in October following a long-term injury, but suffered a first-half knee injury against Aston Villa on Saturday.
“On the positive front, it’s the other knee,” Brown told Hull’s official website.
“On a negative front, we can’t answer the question until we have a complete diagnosis. There is no point in me second guessing what is going to happen over the next 24-48 hours.
“We’ll have more, hopefully good, news on Monday.
“It was disappointing to see one of our main players leaving the field with tears in his eyes.”
