Barlow was assistant to Gary Megson, who quit the club on Thursday, and will take control of the first team along with reserve team coach Ian McParland.
Forest chairman Nigel Doughty is unlikely to make a permanent appointment until the summer.
"It's difficult to envisage a situation where we'll recruit a new manager before the summer," he said.
"Anybody capable or successful is probably engaged with their club at the moment as the season draws to a close.
"We will monitor the situation on a week-by-week basis. But the quality of people who have expressed an interest in the job already has surprised me."
Forest chairman Nigel Doughty is unlikely to make a permanent appointment until the summer.
"It's difficult to envisage a situation where we'll recruit a new manager before the summer," he said.
"Anybody capable or successful is probably engaged with their club at the moment as the season draws to a close.
"We will monitor the situation on a week-by-week basis. But the quality of people who have expressed an interest in the job already has surprised me."