Human Rights Watch also said that at least 40 people, including children, have been killed in the protests, citing Sudanese activists and medical workers.
Protests that first erupted in the provinces on December 19 over a government decision to triple the price of bread have swiftly escalated into nationwide rallies widely seen as the biggest threat to Bashir's three-decade rule.
Although the trigger was the rise in the price of bread, Sudan has faced a mounting economic crisis over the past year, led by an acute shortage of foreign currency. It restricted Sudan from conducting global business and financial transactions.
The United States lifted 20-year-old trade sanctions on Sudan in October 2017, but many investors continue to shun a country still listed by Washington as a state sponsor of terrorism.
Al-Bashir, who has been ruling the country since a military coup in 1989 and remains wanted by the International Court of Justice for war crimes, has blamed the protests against his government on "conspirators".
The crackdown has drawn global criticism, with countries like Britain, Norway, Canada and the United States warning Khartoum that its actions could "have an impact" on its relations with their governments.
Sudan's economy was crippled when the south seceded in 2011, taking away much of its oil resources.