Starc was able to bat and bowl in the remainder of the game but admits he does not know what his recovery timeframe looks like as he needs to consult a specialist in Sydney.
"I'm getting another scan in Sydney and seeing a finger specialist to work through all that," Starc said after Australia wrapped up victory in Melbourne inside four days.
"Obviously India is coming up, so we'll see what the timeframes are after I've had those discussions next week. Hopefully [my return] fits in somewhere at the front end of the tour.
"Apart from the finger being out of action, I can still train to some degree and bowl in creative ways to keep up my workloads up whilst the finger not being impacted. So that side of it is going to be fine. It's just where the timeframe of the tendon comes into it for the India tour.
"From the scans the other day the tendon's basically gone from the top of the finger so I can't straighten it."
Australia likely to name Sydney squad on Friday
Australia's first Test against India starts on February 9 in Nagpur. Starc has not missed a Test match since the 2019 Ashes and was a key part of Australia's last two subcontinent tours when Australia played only two specialist quicks in four of the five Test matches in Pakistan and Sri Lanka, with Green as the allrounder.
India aside, Cummins' immediate concern is replacing both Starc and Green for the third Test against South Africa in Sydney.
"The first thing is to probably have a look at the wicket up there," Cummins said post the MCG win. "From afar it looks a little bit dry this year. I'm sure we'll add an extra spinner to the mix. Greeny is pretty close to being irreplaceable I think as a top order batter that gives you another bowling option. We'll chat through all those combinations when we get a bit closer but we're not settled on anything."
Agar played his first two first-class games in 18 months just recently for the Prime Minister's XI and Western Australia, returning figures of 3 for 212 from 78.4 overs while battling to readjust to red-ball bowling after so much limited-overs cricket.
Cummins admitted Australia could look to trial some players for India in the Sydney Test but acknowledged that they still need to win to shore up their place in the World Test Championship final.
"I think it's a mix," Cummins said, "It's probably going to be the wicket in Australia that closest resembles India, even if it doesn't spin big. So it might give us a chance to have a look at one or two players that will be on that Indian tour ahead of that. But the first priority is of course to win the Test match."
There was no indication of who would replace Starc but McDonald had mentioned on SEN on Wednesday that West Australian quick Lance Morris could be Starc's replacement given his raw pace and striking ability.
"He may be looking like he'll get an opportunity in Sydney depending on the balance of that attack," McDonald said.
"Some painkillers helped," Starc said. "I think it's probably just taking a little bit of the pressure off my middle finger onto the ball, which I think actually helped my seam position. So I might see if they want to leave it detached for a bit longer because it's helping the swing.
"It was just to hopefully play a role and be able to not leave them a bowler down. I'm sure they would have been able to do it, but it would have been a big ask for just Scotty, Pat and Nath [Lyon] to bowl [on their own]. I think Pat came over three balls into that first over of the second innings and said this is going better than we thought and I certainly was of the same opinion. It was just nice to be able to play a role and contribute in that second innings."
Alex Malcolm is an Associate Editor at ESPNcricinfo