Transcription-activator-like effectors (TALEs) are programmable DNA binding proteins widely used for genome targeting. TALEs consist of multiple concatenated repeats, each selectively recognizing one nucleobase via a defined repeat variable diresidue (RVD). Effective use of TALEs requires knowledge about their binding ability to epigenetic and other modified nucleobases occurring in target DNA. However, aside from epigenetic cytosine-5 modifications, the binding ability of TALEs to modified DNA is unknown. We here study the binding of TALEs to the epigenetic nucleobase N6-methyladenine (6mA) found in prokaryotic and recently also eukaryotic genomes. We find that the natural, adenine (A)-binding RVD NI is insensitive to 6mA. Model-assisted structure-function studies reveal accommodation of 6mA by RVDs with altered hydrophobic surfaces and abilities of hydrogen bonding to the N6-amino group or N7 atom of A. Surprisingly, this tolerance of N6 substitution was transferrable to bulky N6-alkynyl substituents usable for click chemistry and even to a large rhodamine dye, establishing the N6 position of A as the first site of DNA that offers label introduction within TALE target sites without interference. These findings will guide future in vivo studies with TALEs and expand their applicability as DNA capture probes for analytical applications in vitro.