Prada was born in Ponferrada, León, Castile and León, and represented Real Valladolid as a youth. He made his senior debut with the reserves in 2008, in Segunda División B.
In 2009, Prada joined another reserve team, Real Zaragoza B from Tercera División. On 8 July 2011 he returned to the third level after agreeing to a three-year contract with Zamora CF.
On 21 May 2015, Prada signed for Cádiz CF as a replacement to injured Andrés ahead of the play-offs. He appeared in three games for the club, before moving to the Austrian Football Bundesliga with SV Ried on 2 July. He made his professional debut 23 days later, coming on as a second-half substitute for Thomas Murg in a 0–3 away loss against SK Rapid Wien; he quickly became a regular starter, and appeared in 27 matches during the campaign.