The US Open champion fought valiantly through the pain but ultimately suffered a 6-2 2-6 6-4 defeat in two hours and 19 minutes.
Raducanu will now wait for more information on her back issue before deciding whether to compete in the upcoming Italian Open.
"I was kind of struggling a bit with my back, to be honest," said Raducanu after the match. "Throughout the week I have been carrying some niggles, and it's kind of just taking its toll.
"I'm not sure what I will do yet, whether I will go home yet or straight to Rome. The plan right now is to still go to Rome.
"I'm not sure when I start. Maybe Monday or Tuesday. I hope it's enough time because it would be a real shame to miss it.
"I'm feeling pretty positive. A lot of the time with me it's just overload and then two or three days' complete rest and I'm OK to start training again."
When asked about the treatment she received during the medical timeout, Raducanu added: "I don't know what magic they worked, but I had a numb back for the second and third set so I couldn't feel anything."
Despite facing an early exit at the Madrid Open, the Brit believes there were many positives to take away from the tournament.
The 19-year-old made her first senior appearance on clay just last month, but showed a lot of resilience in her losing effort against Kalinina.
She said: "I feel like I'm going through this and my body is building with each match I play. That was a great two-and-a-half-hour training session, that's going to build towards me physically developing.
"I'm pretty happy with the progress I have made over the last few weeks and I think I have definitely done something to build on and keep building.
"I feel like my mentality and my outlook to how I'm approaching things right now is a lot better."