Statistical properties of language provide important cues for language learning and may be processed by domain-general cognitive systems. We explored the relationship between implicit statistical learning (the ability to detect statistical regularities in input) and language production. Twenty typically developing (TD) children and nine children with acquired language disorders (ALD) (aged 6 to 18 years) produced ‘Cookie Theft’ picture descriptions. Using a computerized analysis, we investigated statistical properties, such as usage frequency and collocation strength of words and word combinations. Participants also completed a non-linguistic serial reaction time (SRT) task, which tested non-verbal statistical learning. We determined age effects, and compared language production and SRT performance between both groups. Older TD children produced more connected language, more words, less frequent function words, more rare or novel combinations, and showed better statistical learning. Children with ALD produced less connected language, more weakly collocated combinations, displayed less lexical diversity and showed poorer statistical learning. Post-hoc analyses found correlations between statistical learning and statistical properties of spoken language. We discuss study limitations, but note that results are compatible with the view that language production draws on statistical learning and that impairment of statistical learning can be related to language disorders.