Catalysis of the reaction: 2-hydroxy-3-keto-5-methylthiopentenyl-1-phosphate + H2O = 1,2-dihydroxy-5-(methylthio)pent-1-en-3-one + phosphate. 2-hydroxy-3-keto-5-methylthiopentenyl-1-phosphate is also known as HK-MTPenyl-P, and 1,2-dihydroxy-3-keto-5-methylthiopentene as DHK-MTPene.