Brown, who was Allardyce's assistant at Bolton, was first concerned about his mentor's health during a game against Leicester when the managers' hearts were monitored.
Brown said: "It's bad news. We were talking about it on Tuesday night strangely enough at the LMA dinner for the 1,000 league games. Coming back on the train, we were talking about the health of managers.
"Sam uses specialists down in London now and hopefully now they've found it all in time. I remember the last time Sam had his heart checked during the course of a game. It was against Leicester. It was a hell of a game.
"We came back from 2-0 down to 2-2, down to nine men. We got the equaliser in the 93rd minute, it was Michael Ricketts, and then Harry Bassett, who was having his heart monitored, had a blip. He had something wrong with him and he had to step away from it.
"Where Sam was concerned, his heart was running at something like 200 during the course of the game and not doing any exercise can't be healthy for him. I wish him a speedy recovery."