Nearly 21,000 voters had not collected their voting document by the time the deadline last night.
At 11 p. m., 20,840 voting documents remained unclaimed. Voters had until midnight to collect their document from the Electoral Commission offices in Valletta.
The Electoral Commission would not confirm the information, saying it would publish the official count today in the Government Gazette.
The amount represents about seven per cent of the 325,103 eligible voters listed in the October Electoral Register.
The referendum is the sixth in Malta's history with the last one being on EU membership in 2003.
In the EU referendum, 5,161 voting documents were uncollected and in the 2008 general election the figure was 5,266. In the 2009 European Parliament election, 15,578 documents were unclaimed.
Voting tomorrow starts at 7 a. m. and ends at 10 p. m. Vote counting starts at 10 a.m. on Sunday at the Mediterranean Conference Centre.
In a series of instructions issued yesterday, the Electoral Commission notified administrators of old people's homes that the voting document belongs to the person to whom it was issued.
"Whoever is in illegal possession of a voting document would be committing a crime," the commission warned, adding that no influence should be exercised on residents of these homes.
Administrators have to ensure free access is granted to residents who want to vote and to authorised persons accompanying them to the polling places if voters so requested.
It also pointed out that tomorrow only relatives of residents to whom a permit was issued by the commission will be allowed to enter old people's homes.
It also said that every person who "hinders or prevents the free exercise of a voter's right to vote" would be committing a crime.
Voters going abroad on polling day can jump the queue if they present their flight or sea tickets to the police officer in charge.
The campaign was concluded last night with a TV debate organised by the Broadcasting Authority between Deborah Schembri, from the yes movement, and Arthur Galea Salamone, from the no movement.
The law prohibits any campaigning and reporting today and tomorrow.