Leg-spinner Warne, one of the greatest cricketers of all time, died of a suspected heart attack aged 52.
A stand at the Melbourne Cricket Ground will be permanently renamed the SK Warne Stand as a tribute.
Fans left flowers, beer cans and photographs at Warne’s statue at the MCG.
Warne took his first Test hat-trick at the MCG and also claimed his 700th Test wicket at the ground in 2006.
Victorian Premier Daniel Andrews has offered a state funeral to the family of a man who he said “defined a generation”.
“To us, he was the greatest – but to his family, he was so much more. Our hearts are breaking for Shane’s family and friends,” Andrews said.
“I have offered a state funeral to his family so Victorians can pay tribute to his legacy and contribution to our state, community and country.”
State funerals are held to honour people of national significance.
Australian Prime Minister Scott Morrison has also offered his family a state funeral for Warne.
Former Australia batter Ricky Ponting, who captained Warne from 2004-2007, called him “the greatest bowler I ever played with or against”.
“He gave me my nickname. We were teammates for more than a decade, riding all the highs and lows together,” Ponting wrote on Twitter.
“Through it all he was someone you could always count on, someone who loved his family, someone who would be there for you when you needed him and always put his mates first.”
Australia and Pakistan men wore black armbands and held a minute’s silence before play on the second day of the first Test in Lahore.
Australia’s women also wore black armbands in their Women’s World Cup victory against England and observed a silence for both Warne and Rod Marsh, who died on Thursday.
Leg-spinner Alana King touched her armband after dismissing Tammy Beaumont as a mark of respect to Warne.
Cricketers in the Sheffield Shield, Australia’s domestic competition, also wore black armbands and AFL players observed a minute’s silence.
Warne died in his villa on the Thai island of Koh Samui on Friday of a suspected heart attack.
Thai police told Reuters his death was not being treated as suspicious.
