Schools and public attractions have been shut down, while buses were being laid on along the beaches and take people away from the area.
"It's important that those in low-lying areas can get to higher ground," Tammy Mori, the spokeswoman for the state transportation department, told the Honolulu Advertiser newspaper.
"We want to remind people that they have five hours to evacuate after the alarms sound."
'Shores at risk'
The Pacific Tsunami Warning Centre has said that waves up to 4.8 metres could hit the town of Hilo on Hawaii's Big Island from about 11.19am (21:19 GMT).
Waves will then hit Honolulu, the state capital, at 11:52am.
"Urgent action should be taken to protect lives and property," the Warning Center said in a bulletin.
"All shores are at risk no matter which direction they face."
Local media showed lines of people at petrol stations along the busy Kalanianaole Highway on Oahu and in Hilo as residents left for higher ground.
Victor Sardina, a geophysicist at the Hawaii-based centre, said that Hilo Bay was likely to face the worst of the tsunami.
"The shape of the bay favours the waves gaining in height," he told the Reuters news agency in a telephone interview.
Kirk Caldwell, the managing director of Honolulu, said the city was working with hotels to warn tourists in the famous Waikiki beach area to effect a "vertical evacuation," meaning people should move to the third floor or higher.
He said police would close roads in inland areas at 10am, an hour before the first wave is scheduled to hit, to prevent gridlock in flood zones
The 8.8 magnitude earthquake near the city of Concption in Chile earlier on Saturday has triggered a tsunami warning across the Pacific rim, which stretches from Japan to the Antarctic.
"Everybody is under a warning because the wave, we know, is on its way. Everybody is at risk now," Sardina said.