MIAMI -- Eduardo Rodriguez pitched the first two innings of Venezuela's 4-1 victory over Nicaragua in Tuesday's pool-play game, and that will probably be the last time he pitches for his home country during the World Baseball Classic.

Venezuela's manager, Omar Lopez, said after the game that Rodriguez won't be available for any of the next two rounds, as part of a pre-tournament agreement with his major league team, the Detroit Tigers.

Lopez added that he would circle back with the organization in hopes that he might be available for a potential championship matchup on Tuesday, given that Rodriguez is the only starting pitcher lined up. But Tigers manager A.J. Hinch told reporters in Lakeland, Florida, that Rodriguez is scheduled to pitch in a spring training game against the Washington Nationals on Sunday, which would rule him out for the finale a couple of days later.

Venezuela, which has won each of its first three pool-play games, will automatically advance into the second round if the Dominican Republic defeats Israel on Tuesday night. Under that scenario, the Wednesday night game between the Dominican Republic and Puerto Rico would determine the Pool D runner-up.

Rodriguez, who allowed seven hits but only one run, is one of four starting pitchers on Venezuela's roster, along with Martin Perez, Pablo Lopez, Jesus Luzardo and Luis Garcia, the latter of whom was used for multiple innings out of the bullpen on Saturday.

Sources with Team Venezuela told ESPN's Marly Rivera that there are potential limitations from the Tigers on 39-year-old designated hitter Miguel Cabrera the rest of the tournament. A league source familiar with the team refuted the account, saying there are "no restrictions" on his participation. The Venezuela source described conversations with the Tigers as "fluid."