Usually when a person has had a heart attack (damaged heart cells) there may be some loss of the heart's contractual ability to adequately pump enough blood/oxygen into the system to meet the demand. As Flycaster states there is not enough information to answer, but if there is shortness of breath with the exertion that would be a good indication to not exert that degree of physical stress.
If an individual had a mild MI, one should have been told by the doctor or the hospital's discharge information to any conditions or situations to be avoided. Generally, if the person is healthy otherwise and compensating well, there wouldn't be any problem.
You haven't given much information or specifics so it is a difficult question to answer. Do you know what the person's ejection fraction (efficiency level of the heart to pump blood) is rated? If the person has a low ejection fraction, then yes, it is conceivable that mild exercise could be a challenge.