If the virus integrates into the genome than you can use DNA extraction. If the virus remains as episome ... probably, but I'm not sure 100%, depends on the size of the virus genome if you use columns, they have certain length limitations where they don't bind efficiently anymore (loose small genomes in flow-through) or don't elute anymore small DNA length.

We use Qiagen QIAamp Mini kit for total DNA extraction from cell culture including plasmid remains and it works well.

Thanks Ulrike. The genome integrates into the cellular genome in this case and thus, I hope using columns will work.

Roche total nucleic acid kit will give you both DNA and RNA regardless of the size. Then you can choose to RNase out before you proceed if you are confident that your virus will be in DNA state.