In adults epicardium-derived progenitor cells line the heart, but have become dormant.
Scientists used a chemical, thymosin beta 4, to "wake them up".
Professor Paul Riley, from the University College London, said: "The adult epicardial cells which line the muscle of the heart can be activated, move inward and give rise to new heart muscle."
"We saw an improvement in the ejection fraction, in the ability of the heart to pump out blood, of 25%."
As well as pumping more blood, the scar tissue was reduced and the walls of the heart became thicker.
Peter Weissberg, medical director of the British Heart Foundation, said he was "very excited" about the research but warned the scale of improvement seen in animals was rarely seen in humans.
However, he argued that even a small improvement would have a dramatic impact on people's quality of life.
"A normal heart has lots of spare capacity. In patients with heart failure it is working flat out just to sit down [and] it's like running a marathon," he said.
"You could turn a patient from somebody who's gasping while sitting in a chair to somebody who can sit comfortably in a chair."
UK Heart statistics
Deaths from coronary heart disease
1961 - 165,216
2001 - 117,743
2009 - 80,223
Estimated people living with heart failure
1961 - 100,000
1971 - 300,000
2010 - 750,000
Source: British Heart Foundation
The mice needed to take the drug in advance of a heart attack in order for it to be effective. As the researchers put it, "the priming effect is key".
If a similar drug could be found to be effective in humans, then the researchers believe it would need to be prescribed in a similar way to statins.
Professor Riley said "I could envisage a patient known to be at risk of a heart attack - either because of family history or warning signs spotted by their GP - taking an oral tablet, which would prime their heart so that if they had a heart attack the damage could be repaired."
He said this could be available in 10 years.
Epicardium derived progenitor cells (in red) lining the heart
The British Heart Foundation, which funded the study, said repairing a damaged heart was the "holy grail" of heart research.
The results strengthened the evidence that drugs could be used to prevent the onset of heart failure, it said.