I am not aware of any 'universal' DNAse inhibitor, and the usual solutions (lower temperature, use chelating agents, etc.) clearly don't apply here. Can you try perhaps titrating out the contaminant nucleases with double-stranded oligonucleotides? Another shot in the dark would be to reduce disulfide bridges and derivatize them, if your complex can withstand it (many extracellular nucleases contain essential disulfide bridges).

Out of curiosity, is the cleavage site-specific?

another purification step may be necessary. If the degradation is mainly due to the exonuclease activity, the use of oligo with the modification at the ends could help.

Adding additional purification steps is always a good way to try to get rid of nucleases. Also depending on your protein, one way to get rid of some nucleases during purification is to "wash" your protein with a ATP/Mg2+. When your protein is bound to affinity resin (GST or Nickel..) incubate your beads in you wash buffer complemented with ATP/Mg, I usually do 30 min (or longer) at 4C.

Don't do that if your protein has a ATPase activity, though

Thank you all for your answers. I already do 4 purification steps. Nickel two times (before and after TEV cleavage), a GF and an anion exchange. Even after all these steps, the DNA still gets chopped when I add Mg2+. I cannot add reducing agent because I need to preserve a disulfide bond. My protein is an ATPase. The cleavage site does not seem to be specific, as I get different species. I will try to use an oligo modified at the ends.

I experienced that problem once, I was purifying a helicase and it had exonuclease contamination. Are you purifying the protein from Sf9 cell extract ? They are known for this contamination. Since my helicase acts on DNA and is an ATPase, I could not use any nuclease inhibitors. What I found was useful is to saturate the beads as much as I can, even though I lose some protein, I still get rid of the nuclease binding. That was the key, so every time I purify, I use little less beads than the amount of protein. Subsequent purification might also help, but as it is known the more the number of columns you run, the more protein you lose. So, I would rather save my time and lose some protein in the first step. Since you have mentioned that you do have subsequent purification, I suspect the nuclease might be interacting with your protein of interest. Do you digest the DNA in the cell extract ? The interaction might be mediated by DNA.