CPR was administered to Hamlin on the field before he was taken away by ambulance, with a representative saying on Tuesday Hamlin was "fighting" to recover.
Hamlin has been described as being in critical condition at the University of Cincinnati Medical Center, and Brown joined those giving their best wishes to the 24-year-old.
Brown said in a statement: "First and foremost, the Bengals continue to send thoughts and prayers to Damar Hamlin and his family.
"Our hearts are with everyone in this unprecedented time – what we can do is support one another.
"Last night was supposed to be a great night for the NFL and a great showcase for our hometown. Instead, the human side of our sport became paramount… and in that moment, humanity and love rose to the forefront.
"The Bengals are thankful for the love and compassion shown by all. Praying for Damar."
Brown also hailed the medical response to Hamlin's collapse, which led to the game being suspended with the Bengals 7-3 ahead.
He added: "As medical personnel undertook extraordinary measures, both teams demonstrated respect and compassion while fans in the stadium and people around the country bolstered the support for Damar and love for each other."