MACC sources said he is expected, among others, to explain allegations that funds from 1MDB had been used to finance the making of several Hollywood movies.
After the election, Najib and his wife were barred from leaving the country and have been under investigation, according to the AP.
His arrest comes less than two months following Barisan Nasional (BN)'s spectacular defeat in the May 9 general election, and signals the tightening legal noose over Najib and his family as well as his close political and business allies.
AFP says A Malaysian cabinet minister has since said that "Malaysian Official 1" was Najib.
Mahathir Mohamad, Najib's 92-year-old successor who came out of retirement to run for election, told Reuters last month that there was "an nearly flawless case" against the former prime minister. "Wait for our statement", the source said.
A spokesman for the politician did not immediately comment but Najib has consistently denied wrongdoing.
The scandal led to a stunning electoral loss in May of Najib's National Front coalition, which had ruled Malaysia uninterrupted since gaining independence in 1957.
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Allegations over the misappropriation of state funds at 1MBD emerged in 2015 as the public learned that $4bn had gone missing from the fund and almost $700m was allegedly transferred into Najib's bank account. The new Attorney-General Mohamed Apandi Ali cleared Najib in 2016, saying the money was a donation from the Saudi royal family and that most of it was returned.
In this May 24 photo, former Malaysian prime minister Najib Razak speaks as he leaves the Malaysian Anti-Corruption Commission Office in Kuala Lumpur.
At least 10 countries around the world launched investigations on the Malaysian fund, focusing on possible money laundering and embezzlement.
The US Department of Justice has alleged in lawsuits that more than $4.5bn (£3.4bn) from 1MDB was laundered through a complex web of transactions and shell companies, of which $681m ended in Najib's bank account.
Billions of dollars are unaccounted for from the fund, set up by Mr Najib.
The arrest, made in connection with the investigation of a massive corruption scandal, was carried out last week by anti-corruption task force officials.
Malaysian investigators are questioning the producer of The Wolf of Wall Street as they step up efforts to recoup funds potentially lost through 1MDB.