Raducanu was off the pace in a first set in Doha that took just 23 minutes and saw her win just 10 points, although she upped her level in the second.
The Brit was crucially broken for 6-5 by Kalinina but saved two set points to take it into a tie-break, although missed a chance of her own before losing the match.
"I think I was struggling with everything - serve, return, forehand, backhand," Raducanu told Sky Sports afterwards.
"To be honest I felt like I never really got into it. I think it was a combination of things. It's like my first day match I think I've played in a year, so that's different.
"Honestly, I think I need to practice training outside a bit more because it's very different and also the light, conditions, shadows - it's really hard to kind of see the ball, I found towards the end."
It was Raducanu's fourth tournament of the season, while it was her first loss in an opening round since returning from an eight-month injury lay-off.
Kalinina, meanwhile, claimed victory for just the second time this year and improved her head-to-head record with Raducanu to 2-0.
The Ukrainian will face eighth seed Jelena Ostapenko in the second round.