Yes, injury is not a requirement of domestic violence in Michigan. If an injury occurs which requires medical attention, it is aggravated domestic violence which is a more serious charge. A simple straight forward domestic violence simply requires a battery or assault against another without their permission.
This means a push, a shove, a kick, throwing a newspaper, the remote, a wine bottle are all domestic violence. It even means putting someone in the corner, yelling at them and making that person think they are about to be struck can be domestic violence too.
I handle a lot of cases where the extent of the contact is pushing and shoving and it's going both ways, but my client is still arrested. It's up to the "victim" to tell the truth and state it was mutual and not one sided, which is still not a true defense for my client, but a factor which should lead to a more favorable offer and outcome. My clients are shocked when I tell them simply pushing your spouse against their will is a crime. If they called the police then it's a good bet something was against their will.
Many times my clients tell the police "we were pushing each other" or "yes i shoved her but she was trying to do X to me" - those admissions are just as incriminating as telling the cop that you punched your wife right in the nose - they are both domestic violence.