The National League North club shocked Reading 2-1 on Saturday and have been rewarded with a tie at home to the Premier League side, who sit 115 places above them in the football pyramid.
Boreham Wood, the other non-league team left in the competition after beating AFC Wimbledon, have been handed a trip to Championship table-toppers Bournemouth.
League One Cambridge, meanwhile, will entertain Luton for a place in the fifth round following their stunning 1-0 victory at Newcastle.
In some other stand out ties, Plymouth will travel to Stamford Bridge to face Chelsea and holders Leicester City make the short trip to Nottingham Forest
for a Midlands detby after the Championship side knocked out Arsenal.
Liverpool, who overcame Shrewsbury Town on Saturday, will welcome Cardiff City to Anfield.
There are also three full Premier League match ups where Everton will take on Brentford, Wolves will host Norwich City and Tottenham will face Brighton.
Manchester City will play Fulham at the Etihad Stadium, with Manchester United or Aston Villa, who complete the third-round schedule on Monday evening, to welcome Middlesbrough.
The to be played over the first weekend in February.
Undoubtedly the biggest match up to have come from the draw is Kidderminster's tie against Premier League giants West Ham United.
Competing in the national league, the side based near Birmingham overcame Championship outfit Reading in the third round 2-1.
It will also be the second time the two have met with their last meeting occurring in 1994 also in the FA Cup where the Irons secured a 1-0 win at Aggborough Stadium.
In a buoyant mood, the club sent a message to West Ham on social media platform Twitter looking forward to their fourth round tie.
Elsewhere, League Two Hartlepool, competing in round four for the first time since 2009, have been handed a trip to Crystal Palace, while Huddersfield face Barnsley and QPR head to Peterborough.
Southampton will entertain Coventry, while Stoke will play Wigan at home.
FA Cup fourth round draw in full
Crystal Palace v Hartlepool
Bournemouth v Boreham Wood
Huddersfield v Barnsley
Peterborough v QPR
Cambridge United v Luton Town
Southampton v Coventry City
Chelsea vs Plymouth Argyle
Everton v Brentford
Kidderminster Harriers v West Ham
Manchester United or Aston Villa v Middlesbrough
Tottenham v Brighton
Liverpool v Cardiff City
Stoke City v Wigan Athletic
Nottingham Forest v Leicester
Manchester City v Fulham
Wolves v Norwich