Wheldon died after his car became ensnared in a fiery 15-vehicle pileup which appeared to have been sparked when the wheels of two participants - one of them Kiwi Wade Cunningham - touched.
Wheldon's vehicle flew over another race car and hit the catch fence just outside turn 2 in a season-ending race at Las Vegas Motor Speedway.
Dixon, who was driving in yesterday's fatal Las Vegas IndyCar race, said Wheldon was family and he would "miss him badly''.
"Such an amazing person and wonderful family man. We will be with [wife] Susie, [2-year-old son] Sebastian and [7-month-old] Oliver for whatever they need. I still can't believe it.''
Dixon and Wheldon were partnered together when they were both part of the Chip Ganassi team for the 2006 IndyCar season.
Dixon said the 15-car pileup was "just a chain reaction'' and everybody slowed down, got bunched up and "there were more crashes that started behind it''.
"It's unfortunate because everybody knew it was going to happen.
"You could see from lap 2 people were driving nuts.
"It doesn't even matter the speeds - you can't touch with these cars.
"It was pure luck that I wasn't in it,'' he said.
Dixon, the 2008 Indy 500 winner and IndyCar champion, also took to Twitter to express his sorrow over Wheldon's death.
"My dearest friend Danny boy. Thank you for everything! Your an amazing driver and man. I will miss you so badly. Luv ya mate.''
Cunningham said he was truly sorry about Wheldon's death. The Aucklander said "things happen in this kind of racing. It's so close. Not much room for error.''
"I was near the front of what caused all this, so I'm not thrilled about it.
"At this point, whose fault it was is kind of immaterial.''
The green flag had barely stopped waving to signal the end of a caution period when disaster struck.
Wheldon, driving from the back of the field, was in the middle of the pack when he drove into a tangle of cars careering off each other in every direction.
Unable to avoid the massive wreck unfolding before him, he clipped another participant and went hurtling through the air, his car bursting into flames as it flew into the fence.
After just 11 laps, the race was over.
Two hours later, track officials announced that Wheldon was dead.
The English-born 33-year-old won 16 times in his IndyCar career and was the series champion in 2005.
In honour of Wheldon, drivers - many sobbing openly - took part in a five-lap salute around the 2.4km oval as thousands of fans stood and cheered from the grandstand.
Three other drivers, including championship contender Will Power, were hurt in the pileup.
IndyCar has not had a fatality since Paul Dana was killed at Homestead in 2006, during a crash in a warmup. Wheldon won the race later that day.
- Amelia Wade of The New Zealand Herald/AP
