Towers did go on to say that Ross would not play in any more Cactus League games, meaning the team could backdate his stint on the DL so he would only have to miss the first five games of the season.
D-backs manager Kirk Gibson went a little further, saying that it was "likely" Ross would start the year on the DL.
The D-backs open the season with three games at home against the Cardinals before traveling to Milwaukee for a three-game series. They then come home for an extended homestand.
"If he does start off on the DL, we think there's a very good chance we could get him back by the time we get back from Milwaukee," Towers said.
Ross did some light jogging on Tuesday, the first time he has done so since March 3.
With center fielder Adam Eaton already slated to start the year on the DL, the loss of Ross means that A.J. Pollock would make the team and likely start in center with Gerardo Parra starting in right and Jason Kubel in left.
Gibson said in that scenario, either Minor Leaguer Alfredo Marte or Tony Campana would make the Opening Day roster as a backup outfielder.
Steve Gilbert is a reporter for MLB.com. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.