Elliott was unable to finish Tuesday's practice and had his leg stretched out in the middle of the workout. Jones did not have a definitive timetable as to when Elliott would return. But a team source told ESPN's Ed Werder that Elliott will probably miss about a week.
"We'll be very conservative with that in terms of how he feels," Jones said. "Those soft-tissue issues in camp can be tricky, so we've got to make sure that all the soreness is out and he's ready to go before we put him back out there. I don't see him getting back out there, you know. He may miss some time."
The Cowboys return to practice on Thursday and have another off day on Monday. Their first preseason game is Aug. 13 against the Los Angeles Rams.
Elliott had been working with the first-team offense with last year's leading rusher, Darren McFadden, sidelined because of a broken elbow. The fourth overall pick in the draft has made a favorable impression among coaches and teammates with what he was able to do in the spring and early in training camp.
With Elliott and McFadden out, Alfred Morris would move into the first-team role. The Cowboys signed him to a two-year deal in the offseason as a free agent after a four-year run with the Washington Redskins in which he posted three 1,000-yard seasons.
Jones said the Cowboys are not on the lookout for a running back, despite the injuries to Elliott; McFadden, who is on the non-football injury list; and Lance Dunbar, who is on the physically unable to perform list recovering from a knee injury.
ESPN's Ed Werder contributed to this report.