The former Doctor Who star is currently appearing in Shakespeare's Much Ado About Nothing in London, but he had to axe his appearances on both Monday (29Aug11) and Tuesday (30Aug11) after falling sick.
Understudy Alex Beckett took over the role of Benedick in Tennant's absence, but producers are hoping he'll be able to return to the show on Wednesday (31Aug11).
The play at the Wyndham's Theatre is due to finish on 3 September (11).
Tennant's voice problems also forced him to axe a scheduled promotional interview with BBC Radio 1 on Wednesday (31Aug11).
In a post on Twitter.com, presenter Fearne Cotton writes, "Big shame but David Tennant has lost his voice so can't come on my show today. We will get him back on soon though. Get better David!"