Both Hazlewood and Sean Abbott, who was named in the test squad as a back-up fast bowler, went to get scans after bowling for New South Wales on the third day of a Sheffield Shield match against Victoria.
"Hazlewood left the field late in Victoria's innings at the SCG today, reporting tightness in his right hamstring. He underwent precautionary scans which have cleared him of muscle strain," Cricket Australia said in a statement.
"(He) will join the Australian squad as planned in Perth (and) will train as planned in the lead-up to the first test."
With skipper Pat Cummins already out of the series opener because of a back injury, Australia are expected to send out Hazlewood with Mitchell Starc and Scott Boland as their pace attack.
Uncapped Abbott was confirmed as suffering a "moderate-grade hamstring" injury, Cricket Australia said.
"He will not be available for selection for the first test match in Perth and his return-to-play plan will be developed over the coming weeks," the statement added.
Hazlewood, who took 1-22 in his nine overs, did not come out to bat and was clearly limping when he came to shake hands with the other players after Victoria won the match.
Steve Smith, who will lead Australia in the absence of Cummins at Perth, acknowledged it was a nervous afternoon.
"Fortunately it was just some tightness (for Hazlewood) and he's good," Smith said.
"I was like, 'What do we do with Starc? Do we just put him on ice completely?’ It’s hard when you’re playing a game and you want to do well for your state, but then you have an eye on next week.
"I was like, 'Geez, I just don’t want Starcy to get injured (as well).' I told Boland, 'You can bowl one spell and be done as well'," Smith said about Starc and Boland, who play for New South Wales and Victoria respectively.
The first test against England starts at Perth Stadium on November 21 with further clashes taking place in Brisbane, Adelaide, Melbourne, and Sydney around New Year.