The Council of Senators will be an advisory body without legislative powers. It will include 200 elected members and 100 appointed by the president.
As in Egypt's main parliamentary chamber, supporters of President Abdel Fattah al-Sisi are expected to dominate.
Officials say the Senate will enhance political participation, but the build-up to the elections was low key, which commentators attributed to the coronavirus pandemic, a lack of awareness about the new chamber and apathy.
Sisi was elected president in 2014 with 97% of the vote, and re-elected four years later with the same percentage.
Last year, a referendum approved constitutional changes that could allow him to stay in office until 2030, widening his powers over the judiciary and establishing the Senate.
One hundred Senate members will be elected as individual candidates and 100 from a closed list system, where people vote for parties.
The only closed list to be submitted is headed by the strongly pro-government Mostaqbal Watan party, though it included two parties from a coalition that rejected last year's constitutional changes.
"Of course, the government is using us to beautify the picture," by giving the impression of political competition, Mohamed Anwar al-Sadat, who heads the opposition Reform and Development Party, told Reuters.
"We should be realistic ... today in Egypt the space for practicing political work has become narrow."
Nearly 63 million people out of a total population of more than 100 million are eligible to vote, according to state news agency MENA.
Polling stations opened at 9 a.m. (0700 GMT) and will close at 9 p.m., over two days of voting. Results are due on Aug. 19.
Measures to guard against the coronavirus include the sterilization of voting stations and obligatory masks.
Officially confirmed cases of the virus in Egypt have rebounded slightly after a sharp fall, with some officials and doctors warning of a second wave of infections.
Authorities have reported just over 95,000 infections and 5,000 deaths.