Iyer suffered a lacerated spleen during India's victory over Australia in the third one-day international in Sydney on Saturday when he fell awkwardly in taking a catch.
The 30-year-old was admitted to hospital and Indian media reported that his condition was life-threatening.
"We spoke to him," Suryakumar told reporters before India's five-match Twenty20 series against Australia beginning in Canberra on Wednesday.
"When we got to know about his injury, I called him. Then I realised Shreyas doesn't have his phone on him and I called our physio, Kamlesh Jain, who told us he's stable.
"He's looking good (now). We've been in touch for two days, he's replying. If he's able to reply on the phone, then he's stable."
Suryakumar said all-rounder Nitish Kumar Reddy, who was ruled out of the final ODI with a quadriceps injury, was fit.
"He's doing fine, he did a bit of running and batting in the nets yesterday. Today he wanted to take a break as it was optional practice, but we came to the ground because we had a team meeting," Suryakumar said.
India's cricket board (BCCI) said in a statement: "Shreyas Iyer sustained a blunt injury to his abdomen, resulting in a laceration of his spleen with internal bleeding on 25th October during the third ODI against Australia.
"A repeat scan has shown significant improvement, and Shreyas is on the road to recovery."
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