Wade's wife, Samantha, revealed the 39-year-old remains in Germany as he continues to be observed by doctors and awaits further treatment.
The current world number five was in superb form during the European Tour event in Leverkusen as he saw off Berry van Peer, Jose de Sousa and Ryan Searle to seal his place in the tournament's semi-final.
However, before his match with Dimitri Van den Bergh, Wade fell ill and was taken to hospital following the advice of the paramedic team.
A statement posted on Wade's twitter page read: "Following his admission to hospital, Wade underwent a series of tests to establish the cause of serious symptoms including a racing heart, high blood pressure, nausea and dizziness.
"Although the player, one of the most successful ever to compete in the PDC with 11 major titles, is now comfortable and improving, he is being detained by the hospital team for observation and further treatment is currently not fit enough to fly home.
"James' wife Samantha, who has been unable to join James as she is caring for the couple's son Arthur and also expecting their second child, has been extremely grateful for the level of care provided by the German hospital."
Wade is currently enjoying some of his best form in years and is well on track to making the Premier League semi-finals.
The player was scheduled to take part in Thursday's Premier League Darts event in Sheffield.
His wife Samantha added: "It was very worrying on Sunday night and into Monday and it is horrible to think of James there by himself when he has been so poorly.
"Clearly we want him home as quickly as possible, but the medical staff have been amazing with James and he is hugely grateful for the compassion and care that they have shown him - we are taking their advice on when it will be safe for him to return home.
"James is desperate to make sure that he doesn't let anyone down and is already talking about returning to competitive action for the people that have bought tickets.
"Whilst that is his nature, I am sure everyone would agree that him making a full recovery is the important thing and we will be taking it day by day but I know he will be itching to play as soon as physically possible."