Sporting director Dieter Hecking confirmed that Eriksen was expected to rejoin the squad last Friday for the club's friendly against Olympique Lyon before travelling to their pre-season training camp. However, those plans have now been postponed.
"The plan was for him to join the squad for the friendly against Lyon and then travel to the training camp. Unfortunately, that wasn't possible," Hecking said.
"He will soon begin an individual rehabilitation programme in Denmark, and that will likely take some time."
Hecking stressed that Wolfsburg's priority is Eriksen's health rather than setting a timetable for his return.
"We are not going to put pressure on him. It is a very sensitive situation that we are handling with great responsibility."
The club has not given any indication of when the former Manchester United midfielder will be available again, with Hecking admitting he does not know when Eriksen will return.
Eriksen collapsed during Denmark's friendly against Ukraine on 7 June after clutching his chest. He quickly regained consciousness, received treatment on the pitch and was able to walk to the ambulance before being taken to Odense University Hospital.
Heart specialist Henning Molgaard has since told Bold.dk that, in his opinion, the safest option for Eriksen would be to retire from professional football because of the risk of another collapse.
Wolfsburg begin their 2. Bundesliga campaign at home against Kaiserslautern on 8 August, but the club remains focused on ensuring Eriksen makes a full recovery before considering a return to action.