The Irish-born paceman could only send down 8.2 overs before he limped from the Sydney Cricket Ground late in the opening day.
Rankin, 29, who replaced Tim Bresnan in one of three English changes from the side beaten by eight wickets in the fourth Melbourne Test, bowled one ball in his ninth over before he came off for treatment before tea.
He later returned to the field and bowled just one more delivery before again pulling up short. He trudged from the field, reducing the tourists to just three front-line fast bowlers and leg-spinner Scott Borthwick.
Teammate Ben Stokes said later that Rankin's problems had been bad cramping.
"He's fine. It was just a bit of cramp, which is normal in Australian heat, so I think he'll be good to go in the next bowling innings," said Stokes, who took six for 99.
Rankin's setback heaped further pressure on Alastair Cook's squad, who are battling to avoid the ignominy of a 5-0 series whitewash by the Australians.
Cook had early success after winning his first toss of the series, sending the home side into bat and reducing Australia to 97 for five before Brad Haddin and Steve Smith restored the innings with a 128-run sixth-wicket stand.
Australia were all out for 326 and had the tourists at eight for one at stumps.
Ashes: England's Boyd Rankin limps away on Test debut
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