The promise was made by the party’s election strategist Douglas Alexander in a memo last week to supporters, which contrasted the Tories "negative" ads with Labour’s plan to "focus on issues not personalities".
He said: "The Tories have now bought up hundreds of billboard poster sites on high streets across the country for the months of March and April to run their negative personalised adverts.
"We’ll focus our campaign on issues, not personalities – we won’t run any billboard posters with pictures of David Cameron on them."
In the last General Election in 2010, Labour used an image of David Cameron, in a pastiche of TV show ‘Life On Mars’, with the line ‘Don’t let him take Britain back to the 1980s’.
Also this weekend, one of Britain’s biggest brands was brought into the election fray when Boots’ Stefano Pessina said in an interview with the Sunday Telegraph that a Labour victory would be a "catastrophe" and described its policies as "not helpful for business".
Pessina is the acting chief executive of newly-formed Walgreen Alliance Boots, which employs 70,000 staff in the UK and 370,000 worldwide.
The intervention could put Boots’ corporate tax record in the spotlight as Labour chiefs hit back by drawing attention to the fact that Pessina, who lives in Monte Carlo, does not pay tax in the UK. Boots moved its tax residence from the UK to Switzerland in 2007 following a private equity buyout led by Pessina.
Chukka Umunna, the shadow business secretary, said: "The British people and British businesses will draw their own conclusions when those who don’t live here, don’t pay tax in this country and lead firms that reportedly avoid making a fair contribution in what they pay, purport to know what is in Britain’s best interests."