Amid mounting speculation Brown's future at the KC Stadium could be coming to an end, his former striker has twisted the knife.
And with reports circulating that the Tigers chief did not attend training on Wednesday, Windass told talkSPORT Magazine: "I think sometimes you need a fresh change. Phil's done a fantastic job since he's been there but I think it's time that he should get moved on and bring somebody else in."
Hull are currently in the relegation zone in the Premier League and Windass believes a tough season lies ahead.
On being asked if the Tigers can stay up, the former Aberdeen and Bradford forward said: "It's going to be difficult. They're not getting results and they're struggling to score goals at the moment. They need a 10-15 goal-a-year striker to get away from the bottom of the table.
"They've got a little mini league at the moment and it's important they win games against teams in and around their league."
Windass' comments come as accountants raised concerns over the state of the club's finances.
The Tigers' accounts - which were filed five months late - have been assessed by auditors Deloitte, who believe they could be in a perilous position should they lose their Premier League status.
A report warns chairman Paul Duffen and the club's directors they would need to generate a surplus of £23million if the side were to be relegated to the Championship.
If Hull stay up for another season, the accounts say they would still need a £16m surplus to continue living by their current means.
The report warns players would have to be sold in an attempt to balance the books.