The match will be the first at Huish Park in 2017 and a win could see Town progress to the last eight.
The Glovers secured their place in round three with a 4-1 victory over Sky Bet League One outfit MK Dons, while Reading progressed after defeating Southampton on penalties.
Tickets are now available to purchase at the following prices:
Senior/Young Person/Disabled: £5
Tickets can be purchased via the Huish Park ticket office either in person, online or by calling 01935 847888.