CAIRO—Egypt’s government has intensified a crackdown on political opponents, arresting a series of high-profile dissidents in raids on their homes in recent weeks as President Abdel Fattah Al Sisi prepares to begin a new term next month.

Those detained in the current sweep are among the country’s most prominent non-Islamist activists, including three human rights advocates, a satirist, and a well-known labor lawyer.

The...