The 33-year-old suffered several broken bones after suffering an accident while leading the Superbike race at the Ulster Grand Prix last weekend.
Despite his injuries it has been reported that Martin has already signed himself out of hospital in Belfast.
A spokesman for Triumph said Martin was "central" to their record attempt.
The TT racer and television personality from Grimsby, Lincolnshire, is planning to beat the current 376.363mph record (605km/h) in Triumph's 1,000 bhp Rocket III Streamliner.
A spokesman for Leicestershire-based Triumph said: "Guy is a unique talent and having such a pilot is absolutely central to our attempt.
"We wish him a full and speedy recovery and will confirm a new date for our 2016 bid as soon as we can."
On Monday, Martin tweeted: "I'm on the mend - few upgrades to me hand& back but feel right enough. All part of the job. Thanks very much for the support as always."
He is reported to have fractured a vertebrae, his sternum, and a number of ribs in the 100mph crash as well as damaging his throttle hand.
A British team has postponed its bid to break a 400mph land speed record after pilot Guy Martin crashed during the world's fastest road race.