The Bucks face a 400-mile round trip to Suffolk side Felixstowe & Walton United in the second round later this month.
Dennis Greene's side will be strong favourites against their hosts, who play two divisions below Telford in the step four Isthmian League Division One North.
The tie will take place at the home side's Felixstowe-based Dellwood Avenue on Saturday, November 27.
Felixstowe & Walton – nicknamed the Seasiders after the club's setting, where there is the largest container port in the United Kingdom – are 14th in their division, which plays at the equivalent of Market Drayton Town's level, albeit they have games in hand on other sides due to cup commitments.
Cup action could be a welcome break from trials and tribulations in National League North for Telford, after back-to-back league defeats saw the Bucks slip to third-bottom, level on points with their basement rivals.