After the protesters dispersed, clashes continued in other parts of the city.
Around 100 people were apprehended and at least six were formally arrested, according to Ewa Westford, a police spokeswoman.
No injuries were reported.
About 7,000 people gathered at a square in the centre of the city for a peaceful protest, with speakers condemning Israel's offensive in Gaza and urging support for the Palestinians.
As they marched towards the arena, they were joined by the masked demonstrators who attacked police with eggs, rocks and firecrackers.
About 1,000 police were deployed in Malmo to keep the protesters from entering the arena. Special riot vehicles had been brought in from Denmark.
Henrik Kallen from the Swedish Tennis Federation spoke to Al Jazeera from inside the arena. He said the match had not been disturbed.
"I can't comment on if it was right or wrong to from a security stand [to ban fans from the match] but what is unfortunate is that some local politicians have used it for their own agenda, mixing sports and politics and making national politics out of something they should not get into."
Since Israel's three-week war on Gaza ending in January, activists and politicians have called for the game to be stopped.
The municipality of Malmo said its decision that the match be played in an empty arena was taken due to security concerns, without any political motives.
But Ilmar Reepalu, the mayor of Malmo, told the newspaper Sydsvenska Dagbladet after the war on Gaza that his personal opinion was that the game should not be played at all.
The three-game tie started on Friday with about 300 journalists, sponsors and special guests present in the 4,000-capacity hall.
"It didn't feel like a Davis Cup match, it felt like a challenger match," said Harel Levy, one of the Israeli players.
"It's sad, I think it has affected Sweden more than Israel. Hopefully it will never happen again."
Malmo, which is home to a large number of immigrants, many of them from the Middle East, has been heavily criticised by the International Tennis Federation and Israeli players for its decision to close the tie to the public.
It is the second time that a Davis Cup tie has been held without spectators. The first was in 1975, also in Sweden, when the Swede Bjorn Borg and his team beat Chile, which was ruled at the time by dictator Augusto Pinochet.