Ouma was found guilty by Match Referee Mike Procter in a hearing that took place after the conclusion of the match.
Ouma was found to have breached clause 1.2 of the ICC Code of Conduct which relates to "abuse of cricket equipment or clothing, ground equipment or fixtures and fittings."
The incident in question took place in the 26th over of Kenya's innings when, after being caught and bowled by Kyle McCallan, Ouma slapped his bat against his pad and then kicked the bat a few metres in disappointment as he walked towards the pavilion.
The wicketkeeper-batsman pleaded guilty in the hearing.
All Level 1 breaches carry a minimum penalty of an official reprimand and a maximum penalty of 50 per cent of a player's match fee.
In the case of Level 1 breaches, the match referee's decision is final and a player does not have a right of appeal.
The charge was brought by umpires Peter Hartley and Ian Ramage.
Procter reached his conclusion after a hearing attended by the player, the two on-field umpires, third umpire Alan Neill, Kenya manager Davinder Singh and captain Steve Tikolo.
Ireland won the first of three-match ODI series by 33 runs. The second match at the same venue was washed out while the third and final tie is scheduled to be played on Wednesday.