Jones' sports manager Liam Pickering confirmed the commentator was safe but thinks he should return home.
Jones was commentating in Kabul for the Shpageeza Cricket League, Afghanistan's T20 tournament, when the bomb went off outside the gates.
Australia's Dean Jones in a file picture.
There was no immediate claim of responsibility or details of the players.
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The Shpageeza tournament, now in its fifth season, is one of a small number of Western-style sports competitions along with Afghan Premier League football that have grown up since a US-led campaign toppled the Taliban in 2001.
Basir Mujahed, spokesman for the police in Kabul, told Anadolu Agency, a suicide bomber detonated his explosives when stopped at the first ring of security outside Alakozay International Cricket Stadium.
There were no immediate details on the casualties but Tolo News Television quoted the Afghan Cricket Board as saying all players were safe.
Cricket has gained phenomenal popularity in war-riddled Afghanistan with the national team cruising to gain worldwide status and joining the top 10 teams in the world within years of arrival of the game in the country.
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