A 10,000-strong crowd protested Saturday in the capital, Baku, asking the prime minister to step down, the BBC reported. Parliament last week approved the appointment announced by his seriously ill father, President Heydar Aliyev.
The approval paves the way for Ilham Aliyev to succeed his 80-year-old father, which opponents reject. They want free elections.
Heydar Aliyev is now in a hospital in the United States, being treated for heart problems.
The protesters Saturday carried banners reading "Down with monarchy" and "Elections should be free".
On Friday, the BBC said 10 opposition supporters were arrested during clashes with police and more than 20 protesters have been on hunger strike since Ilham Aliyev was sworn in.