Tuples extraction is a fundamental task for information extraction and knowledge graph construction. The extracted tuples are usually represented as knowledge triples consisting of subject, relation, and object. In practice, however, the validity of knowledge triples is associated with and changes with the spatial, temporal, or other kinds of constraints. Motivated by this observation, this paper proposes a constrained tuple extraction (CTE) task to guarantee the validity of knowledge tuples. Formally, the CTE task is to extract constrained tuples from unstructured text, which adds constraints to conventional triples. To this end, we propose an interaction-aware network. Combinatorial interactions among context-specific external features and distinct-granularity internal features are exploited to effectively mine the potential constraints. Moreover, we have built a new dataset containing totally 1,748,826 constrained tuples for training and 3656 ones for evaluation. Experiments on our dataset and the public CaRB dataset demonstrate the superiority of the proposed model. The constructed dataset and the codes are publicly available.