The Polish player was leading Akgul Amanmuradova of Uzbekistan 6-2, 3-3 when rain interrupted play. The match had failed to get under way on Tuesday due to heavy rain and lightning.
The delays mean the winner of this match may have to play twice on Thursday, as the victor has been scheduled to meet Karolina Pliskova of the Czech Republic in a second-round match.
Meanwhile, Taiwan's Su-Wei Hsieh, who is in the top half of the draw with Radwanska, qualified for the quarter-finals after beating Casey Dellacqua 6-1, 7-5.
Hsieh and fifth seed Petra Martic are the only two players to make it into the quarter-finals so far as all other games were stopped Wednesday. Matches resume Thursday an hour earlier and on three courts to catch up.
Hsieh, who made it through from the qualifying round a day earlier, said she was a little surprised at the ease of her victory as she was suffering from jetlag after arriving in Malaysia from Dubai early Sunday.
"I didn't have much sleep the last two days and in fact took advantage of the three-hour rain delay to get some much needed rest," Hsieh said.
She said her body was still adjusting, and added: "I'm just happy to get to the quarter-finals."
Dellacqua of Australia ranks 107th in the world, while Hsieh is 123rd in world rankings.
Also through to the next round is Croatia's Martic, who overcame a three-hour rain delay before finally taming Kurumi Nara of Japan 6-2, 3-6, 6-0.
The $220,000 BMW Malaysian Open at the Bukit Kiara Equestrian and Country Resort will end on Sunday.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional