Reece was under observation for two days in Kettering hospital before being released on Sunday and was due to see a cardiologist this week to find out when he can resume playing.
The 26-year-old , who pulled up while bowling on the opening day of the Division Two fixture, has been diagnosed with a viral infection which caused inflammation around his heart.
Derbyshire’s director of cricket Kim Barnett said: “Fortunately there wasn’t anything devastating found but he had chest pains and his dad recently had a heart attack so all that made it a worrying situation.
“He had two days in hospital and there was some suggestion he could stand out there with a runner but that was seen as too risky. They think it’s a virus and he’s been put on a course of antibiotics.
“Luis is being monitored to see how the medication works and when he starts to train again he will be kept an eye on but we are hoping it’s a one-off episode and he will soon be back to full health.”
Derbyshire now have a two week break before they play a County Championship game under floodlights in Cardiff and Barnett said: “We hope he might come into consideration for the Glamorgan game but if not then for the T20 squad.”
Reece described what happened when he bowled his second over in Northamptonshire’s first innings.
“I bowled a ball and then found it quite hard to catch my breath and as I walked past the umpire I said ‘I’m struggling to breath.’
“He asked me if I was ok and I said yes but a couple of overs later I had this tightening in my chest and breathing became harder which was when I had to call the physio on.
“It was a bit weird really because although no one was particularly worried, no one knew what was going on. I had four paramedics look at my ECG’s and there was an irregular spike in my heartbeat which luckily was fine but it was an uncertain time.
“It was only when I went into the cardiac unit they found some inflammation round the sac of my heart which they think is a viral infection and there was some fluid there which caused the tightening in the chest.
“The next step is I’m getting referred to a cardiologist to get a review on the situation but I can’t do any strenuous exercise for a week while the inflammation goes down and I’m hoping then we can get a plan as to when I can come back.
“I’m hoping it’s not going to be a long lay-off and as soon as the infection is cleared up I’m good to go. Hopefully I’ll be available for the next game but I’ll know more when I’ve seen the cardiologist.”