The 24-year-old Ivory Coast international dropped to the ground in the 70th minute of Sunday's match, which was abandoned after Ndicka, who remained conscious, left the field on a stretcher.
"He's doing well. A collapsed lung is a painful thing but luckily, if we can say that, he's not suffering from what we feared when he collapsed on the pitch," De Rossi told reporters.
Roma earlier this week ruled out heart problems as the cause, and Ndicka was pictured smiling while sat upright in his hospital bed just hours after the incident.
He spent a night under observation before returning to Rome, with tests revealing no sign of cardiac issues, but instead "a thoracic trauma with minimal left pneumothorax (trapped air between the lung and chest wall)."
Sunday's match was level at 1-1 when it was suspended. The final minutes will be played at a later date, which has yet to be confirmed.
De Rossi said the call to abandon the match was the only feasible decision.
"It's what had to be done, it was an unanimous decision, a normal one even. None of my players were ready to restart the match because the electrocardiogram (done at the stadium) suggested that he had suffered a heart attack."
No date for Ndicka's return to training has been given.
Roma are at home to AC Milan on Thursday in the second leg of their Europa League quarter-final, holding a 1-0 lead in the tie.
As a result of the Ndicka scare, Roma are organising an initiative to offer free heart screenings to supporters over the age of 45 at a local hospital ahead of their next home league game against Bologna on April 22.
