The band - which also includes Marcus Mumford, Ben Lovett and Winston Marshall - announced they are postponing three upcoming US shows this week, but hope to continue with the rest of their summer shows.
One worry is Ted's health scare could jeopardise the band's headlining slot at Glastonbury festival later this month - one of their biggest concerts to date, watched by an estimated 170,000 people on site and a TV audience of millions - but the group are adamant he will make a quick recovery.
They continued: "Sadly we have to postpone three upcoming [US] headline shows planned for this week in Dallas on Tuesday, Woodlands on Wednesday, and New Orleans on Thursday.
"All dates will be rescheduled and will be announced as soon as we can; all tickets for this week's events will be honoured at their rescheduled dates.
"We have no plans to cancel or postpone any other appearances along this current tour. We're all wishing Ted a speedy recovery."
- Bang! Showbiz