Murray was oblivious to the issue, with the second seed facing Portugal's Joao Sousa on Margaret Court Arena when Sears was treated.
Ivanovic left the court and was visibly concerned following Nigel Sears' fall.
Two days ago, Ivanovic was also left shaken when a patron fell down a flight of stairs during her Open win over Anastasija Sevastova.
Ivanovic was leading 4-3 in the first set when play was delayed for 26 minutes while the spectator received medical attention from a health professional in the crowd.
The players remained on court for most of the delay but were headed for the locker room when they were advised to return as the fan was taken from the area on a stretcher.
"I felt really bad, I was actually shaking, because the sound of the lady falling was really loud ... I stopped immediately," Ivanovic said on Thursday.
"Maybe it's not a good tendency to think of the worst but it didn't sound so good."
Bernard Tomic's first-round match against Denis Istomin was also delayed for more than 20 minutes while a woman received medical treatment in the crowd at Hisense Arena.
"It was a very difficult situation to be in ... even the referee I spoke to said it never happened before," Tomic said.
"At one stage, I was looking directly at the lady. It was not a good moment ... I felt very sad."
Murray's wife Kim Sears is due to give birth in February.
The Scot has said he would leave Melbourne mid-tournament should Sears go into premature labour.
- AAP
