Jones told reporters Tuesday that Smith is unlikely to play this week against the Green Bay Packers, but said he liked what he heard regarding Smith's injury.
"We got the best news we could possibly get," Jones said on 105.3 The Fan in Dallas. "We couldn't have asked for better news. Looking forward to having him back out there quick."
Smith suffered the ankle injury late in the fourth quarter of the Cowboys' loss to the New Orleans Saints on Sunday night. Dallas quarterback Dak Prescott was sacked and fell on the left tackle, causing his leg to buckle.
Backup offensive lineman Cameron Fleming replaced Smith for the remainder of the contest. League sources told NFL Media on Monday that Smith is expected to miss only one week due to the ailment.
The Cowboys selected Smith in the first round (No. 9 overall) of the 2011 NFL Draft out of USC. He is a six-time All-Pro selection and six-time Pro Bowl choice.
The Cowboys will host the Packers on Sunday at AT&T Stadium in Dallas.