The Glovers drew 2-2 with the Moors at Huish Park at the weekend forcing a replay at Damson Park to be played the week commencing 14th November.
Potential Second Round opponents Luton beat Exeter City 3-1 in the First Round, thanks to strikes from Danny Hylton (x2) and Glen Rea.
Town have already travelled to Kenilworth Road this season in Sky Bet League Two, coming away with a point thanks to Tom Eaves’ second half equaliser.
Manager Darren Way was quick to point out the work still to be done before turning attentions to the Second Round.
"We’ve still got a big, big job to do with the replay, so we certainly won’t be getting ahead of ourselves.
"I’ve enjoyed both matches at Luton going up against Nathan Jones who I obviously know really well and we would relish the challenge, but our focus is on the replay and going up against a buoyed Solihull Moors side at Damson Park."
All ties are to be played over the weekend of December 2nd – 5th.