World No. 13 Konta, who made it to the semifinals of the tournament in 2016, was the first big-name player to be knocked out of the tournament Tuesday when Tunisia's Ons Jabeur thrashed her 6-4 6-2 in just over an hour on 1573 Arena.
Konta has been troubled by a knee injury for more than a year and had not played in more than four months as she tried to regain her fitness ahead of the season opening Grand Slam.
Edmund, also a previous Australian Open semifinalist, is also out of the tournament after being beaten by Dusan Lajovic in straight sets.
With heavy rain in Melbourne seeing play suspended on the outer courts on Monday, play resumed early in the morning with Edmund 5-2 up in the first set, but the British No. 1 lost the first three games after play resumed to hand Lajovic a route back into the first set.
The Serbian would eventually take the set on a tiebreak before going on to take the match 7-6 (7), 6-3, 7-6 (4).
Information from Reuters was used in this report.