The former Tottenham playmaker had suddenly dropped to the ground at the Parken Stadium as he ran back from the Finland penalty area, leaving players from both teams in clear distress.
English referee Anthony Taylor immediately called medics on to the pitch and Eriksen underwent prolonged treatment, with compressions performed on the chest of the Denmark midfielder before being taken to hospital for further treatment.
It had been a bright opening by the hosts in the Group B fixture, with Finland keeper Lukas Hradecky saving from Jonas Wind and then a header from Tottenham midfielder Pierre-Emile Hojbjerg.
Shortly before half-time, the match was then suspended after Eriksen collapsed.
The Inter midfielder was eventually taken away on a stretcher for further assessment at hospital, where his condition was said to have stabilised.
UEFA confirmed players from both sides requested the Group B fixture be finished on Saturday evening, restarting at 08.30pm local time (1930BST).
After both sets of teams were applauded back on to the pitch, the remaining five minutes of the first half were played out at a low tempo ahead of a short half-time break.
Finland took the lead in the 58th minute when Bayer Leverkusen forward Joel Pohjanpalo headed past Kasper Schmeichel, who could not keep the ball out.
The hosts were awarded a penalty in the 74th minute when Yussuf Poulsen was brought down by a sliding challenge from Paulus Arajuuri, with contact from the defender's knee appearing minimal.
Hojbjerg, though, saw his spot-kick saved as Hradecky dived low to his left.
Vestergaard sent in a low cross through the six-yard box, but Skov Olsen was denied by a saving tackle from Finland's Robin Lod as there was to be no fairytale ending for Denmark.
Denmark will be looking to get their Euro 2020 campaign back on track when they face Belgium on Thursday.
It promises to be another tough test for the Danes as Belgium are one of the hot favourites to win the entire competition.
Finland, meanwhile, will return to action a day later when they face Russia at the Krestovsky Stadium in St. Petersburg.
A win over the Russians would surely seal Finland's place in the Last 16 stage of the tournament.