Various interviews and features on programmes including Daybreak, Loose Women and This Morning have been axed, The Mirror claims.
> The Voice UK vs Britain's Got Talent: Which show was best? - Poll
The Voice UK coach Danny O'Donoghue was due to appear on Daybreak this morning (March 30), but his interview was allegedly cancelled.
This Morning host Holly Willoughby has also reportedly been told to not discuss her other presenting gig on The Voice UK.
An ITV source said: "Instructions have come from the very top at ITV - nothing on the network is allowed to promote The Voice in any way.
"The bosses have gone ballistic that shows on our channels have been plugging a rival. ITV are doing everything they possibly can to make sure The Voice isn't the huge hit the BBC hopes for."
Another insider at the channel also alleged: "The BBC regularly bans our stars from promoting ITV shows on their channel."
Britain's Got Talent and The Voice UK launched on Saturday (March 24) to huge ratings.
The Voice UK has beaten its ITV rival in terms of online searches since its launch on Saturday.
> 'The Voice' UK premiere: Live blog
> 'Britain's Got Talent' 2012: Series premiere - live blog