The Astros announced Smith underwent surgery Tuesday to repair his Achilles.
He signed a two-year, $15 million contract with Houston in December 2017. He compiled a 3.74 ERA and 1.01 WHIP with 46 strikeouts in 45.2 innings across 56 appearances in 2018.
The 34-year-old Ohio native has been one of MLB's most durable relievers since making his debut with the New York Mets in 2007. His 670.1 innings over the past 12 seasons ranks fifth among relief pitchers, according to FanGraphs.
Smith made stops with the Cleveland Indians, Los Angeles Angels, Chicago Cubs and Toronto Blue Jays in between his time with the Mets and Astros.
The journeyman right-hander will probably need a rehab assignment once he completes his recovery, which means the best-case scenario for his return to the majors is likely after the All-Star break in mid-July.
Meanwhile, Ryan Pressly and Hector Rondon figure to handle the set-up work ahead of closer Roberto Osuna for Houston during the season's first half.