Healy was a late withdrawal from the Sydney Sixers ahead of their 42-run defeat to Sydney Thunder in the Women's Big Bash League (WBBL) on Sunday.
The Sixers said Healy had hand surgery after a "domestic accident at home", but her Australia team-mate Phoebe Litchfield later revealed the injury was due to a dog attack.
Healy said on Monday she suffered an injury after putting her hand between her two Staffordshire bull terriers.
"The positive sign out of it is there was no bone or tendon damage, or a rupture," she told reporters in a video conference.
"I think there was an artery involved which probably made it look more like a crime scene than it needed to be. It was quite gory.
"When I pulled my finger out initially, I thought I was in strife. But it's all gone smoothly at the moment."
Healy posted a picture of herself with a bandaged hand on social media on Sunday, saying she appreciated "all the love" from supporters and was watching Sunday's game from home.
Cricket Australia's website said she was in doubt for the rest of the WBBL season but Healy was hopeful of returning to the Sixers before the end.
She will meet with surgeons on Thursday.
"I'd say it's shorter term more than long term at the moment," she said.
The niece of former Australia wicketkeeper Ian Healy and wife of Australia fast bowler Mitchell Starc, Healy has stood in as captain of the national women's team during long-serving skipper Meg Lanning's extended absence. She led Australia to retain the women's Ashes in England in July.
Healy now has a finger injury to rival her husband's bizarre ordeal last year.
Left-armer Starc, who is currently in India for the World Cup, tore open the index finger on his bowling hand on a shoe spike during his follow-through in a T20 match against Sri Lanka and ended up missing a slew of white-ball matches.
