Clint Dempsey and Brad Friedel will face the Swiss power, while the Champions League holders meet Russian opposition in the next round.
Tottenham was paired with Basel in Friday's Europa League quarterfinal draw in Nyon, Switzerland, as the eight remaining teams learned their fate.
Champions League holders Chelsea battled back to eliminate Steaua Bucuresti and will have to deal with Russian outfit Rubin Kazan, who saw off Levante in the round of 16.
The other English side remaining, Newcastle, will have to contend with Portuguese power Benfica, and Lazio will play Fenerbahce to complete the round.
Tottenham, Chelsea, Benfica and Fenerbahce will host the first leg of each tie on April 4, with the return matches taking place one week later. The Europa League semifinal draw will be made on Friday April 12, with ties to be played on April 25 and May 2.
This year's final will be held at the Amsterdam ArenA on May 15.