Far-right party Vox had come to the defence of the man, calling him a “hero” for “having helped a woman” whose purse was stolen by the thief in February 2015 in the southern town of Fuengirola near Malaga.
But rightwing newspaper El Mundo reported that the man, identified as Borja W.V., “took justice into his own hands” and urged respect for the law.
On Monday, the court in Malaga that initially handed out the jail sentence said it had decided to suspend it for four years, during which Borja cannot commit another offence.
In February 2015, Borja, then aged 22, chased and punched a man in the head who had just stolen the woman's purse. The man died two days later from a brain hemorrhage.
The Malaga court in December 2018 sentenced Borja to two years in jail and ordered that he pay €180,000 ($200,000) in compensation to the victim's two daughters.
An appeals court upheld the ruling in April.
In Spain prison sentences of two years or under do not usually result in prison time being served if the convicted person has no previous criminal record.
But by June, Borja had only paid €6,000 and was facing jail.
Vox last week launched a crowd-funding campaign to help him pay and avoid jail, shining a spotlight on the case.
On Monday, the Malaga court said that apart from suspending the jail sentence, it had ordered Borja to pay €250 a month in compensation, if he has the means to do so.
The judge noted that he had not committed another offence since the incident and was not a “criminal risk”.