Muralitharan, who is recovering from shoulder surgery in Sri Lanka while his teammates tour New Zealand, told the newspaper he had spent the weekend in the southern coastal city of Galle handing out cricket bats to underprivileged children with his manager Kushil Gunasekera.
Just minutes after Muralitharan drove out of the city, Galle was devastated by tidal waves triggered by a massive undersea earthquake thousands of kilometers away in Indonesia.
Sri Lanka was the worst hit of several nations stricken by the waves, with nearly 11,000 dead, many missing and hundreds of thousands left homeless.
"I missed the wave by 20 minutes," Muralitharan was quoted as telling the newspaper.
"I had only just left Galle, so I am very lucky to be alive," he said.
"The wave was over 20 feet (six metres) high and it went two kilometres inland (more than a mile).
"A lot of our cricketers are from there and we don't know how their families are. My manager barely survived. His house is gone," he said.
"Galle is totally under water and a lot of people are missing or dead. There are people everywhere screaming."
Team manager Brendan Kuruppu, speaking in Napier, New Zealand, said one player had lost a relative in the disaster.
New Zealand agreed to postpone a one-day international scheduled for Wednesday in Napier so the Sri Lankans could observe five days of national mourning declared for the tsunamic victims.
The remainder of their tour -- four ODI's and two Tests -- will be rescheduled, officials said.
Muralitharan said it would be difficult for him to join his teammates ahead of the first Test against New Zealand in Hamilton, which had been scheduled for January 15, given the extent of devastation in his homeland.
"Something like this has never happened to my country," he said.
"In my opinion, it is not the right time for cricket."