Whichever club wins through to the third round will receive £30,000 in prize money.
Alfreton booked their place in the second round of the competition on Saturday with a 4-2 win over Bury Town, while the Iron were 3-1 victors at Walsall.
They are managed by the former Chesterfield manager Nicky Law, and have the former Scunthorpe players Tommy Evans and Paul Ellender in their squad.
Leeds United will face a tricky trip to Blue Square Premier League side Histon in the second round of the FA Cup later this month, if they can beat Northampton Town at the Sixfields Stadium in a first round replay.
The Cambridgeshire side, who have the former Cambridge United manager John Beck on their coaching staff, are currently fourth in their league and beat Swindon Town 1-0 in the first round.
Curzon Ashton, who beat Exeter City 3-2 on Saturday, face a trip to Kidderminster Harriers in the second round while Blyth Spartans, who beat Shrewsbury Town, have to make the long trip from the North-East to face the South Coast-based Bournemouth.
Draw in full: Chesterfield v Darlington/Droylsden; Peterborough v Accrington/Tranmere; Eastwood v AFC Wimbledon/Wycombe; Notts County v Kettering/Lincoln; Leicester City v Hereford/Dag & Red; Eastbourne/Barrow v Brentford; Bradford v Leyton Orient; Telford/Southend v Luton/Altrincham; Forest Green v Barnet/Rochdale; Histon v Leeds/Northampton; Scunthorpe v Alfreton; Torquay v Oxford/Dorchester; Leiston/Fleetwood Town v Brighton/Hartlepool; Morecambe v Cheltenham; Gillingham v Yeovil/Stockport; Millwall v Aldershot/Rotherham; Carlisle/Grays Ath v Crewe; Bournemouth v Blyth Spartans; Kidderminster v Curzon Ashton; Port Vale v Macclesfield
