Barbados-born Archer staked his claim to play against Australia at Lord's next week by taking six wickets and hitting a century on the opening day against Gloucestershire's second string.
But, as he continues his rehabilitation following a side strain, the 24-year-old failed to repeat that form in the second innings, taking one for 78 from his 19 overs in the eight-wicket win.
Despite posting disappointing figures against youthful opposition on Wednesday, Archer's availability and additional red-ball action will provide a welcome boost for his country after Warwickshire's Stone suffered an injury in training which is expected to keep him sidelined for at least a fortnight.
Stone's enforced absence further depleted England's seam bowling options as he joined James Anderson and Mark Wood on the treatment table, while spinner Moeen Ali is struggling for form.
Warwickshire sport director Paul Farbrace said Stone was due to undergo a scan before a full course of treatment could be determined.
"It's really disappointing for Olly that he's been ruled out of action for such an important two weeks of cricket because of a re-occurrence of his back injury," Farbrace told the county's website.
"In the meantime, he needs to rest up before he can get his body strong again and ready to deal with the demands of being a fast bowler."
Stone, 25, made his Test debut against Ireland last month and was in the squad for the first Ashes contest at his home ground Edgbaston, but did not play in the heavy defeat by Australia.
Anderson, England's record wicket-taker, broke down after just four overs in that match due to a calf injury and did not bowl again.
Archer, meanwhile, was left out of the series opener having required painkillers to play in the World Cup.
His cameo at Blackstone Academy Ground in rural Sussex has so far come without visible evidence of any lingering injury issues.
Sussex coach Jason Gillespie declared on Tuesday that Archer was "100 per cent" fit and expressed surprise that the player was not selected for the Ashes opener.
After conceding 43 runs from his opening eight overs, Archer deployed extra bounce to finally make a breakthrough in his 11th over of the day.
His pacey delivery produced a defensive edge from George Drissell which flew into the hands of Marcus Campopiano at gully.
Archer, who ripped through the visitors' batting line-up before making 108 on the opening day, encountered far more resistance on Wednesday.
He conceded a series of early boundaries, including being hit for six by Gloucestershire opener Greg Willows.
The speed of Archer's deliveries appeared to increase as the day went on. Willows felt the bowler's full force after being caught in the hip area, while Matt Brewer, batting at number eight, was twice struck on the helmet.
