In December, Abdullah Badr was sentenced to a year in prison and fined for his remarks about Elham Chahine on el-Hafiz TV, which is associated with the ultraconservative Salafi movement.
MENA says his appeal was rejected earlier this week and police arrested him Wednesday in the Delta Sharqia province after he failed to turn himself in.
Chahine sued Badr after he accused her on his show of "practicing prostitution" and teaching Egyptian women how to "be immoral and commit adultery." His remarks came after she criticized radical Islamists for their view of the arts.
Chahine's lawyer complained the actress had been exposed to "insults, cursing and humiliation."