They also activated infielder Tommy La Stella from the 60-day disabled list and optioned him to Triple-A before Tuesday's game against the Milwaukee Brewers.
The 38-year-old Ross was placed on the bereavement list on Saturday following the death of his grandmother. He was batting .189 in 51 games.
Szczur is hitting .217 in 35 games for Chicago.
La Stella, acquired from Atlanta in November, has been limited to two games with the Cubs because of a strained right oblique. He was injured April 10, went on the DL four days later and aggravated it in May.