Jupp has been diagnosed with a leaking appendix, and is currently recovering at home following a second operation in 2 March.
"Still, the tour's going ahead and we're all thankful that Tim's now recovering well at home," the band wrote on their website.
The Worship Revolution Tour features legendary artists Rebecca St. James and Vicky Beeching.
Prior to the tour, which kicked off 14 March, Australian-born St James comments: "One of the things that I hope people will sense on this tour is the unity between those of us onstage in our desire to encounter God and bring them together with us into His presence.
"I pray that the love of God will be strongly evident and it will be a powerful experience - more than a concert - it will be an experience that will change lives."
Martin Smith of Delirious? said: "We need a 'worship revolution' every day to remember what it's all about. Our job as musicians, worship leaders and artists is purely to lift up the name of Jesus and let people see Him for who He is.
"We want to create an atmosphere in which people can come with their hearts and tell Him that's He's amazing."
Delirious? kicked off the new year with an international tour, making stops this month in Singapore and India, cities including Bangalore, Cochin, and Pune.
This follows the band's performance in India last year, where they performed before 1.2 million while touring with dynamic US preacher Joyce Meyer. Another tour with Meyer awaits them this year.
