Suboxone is not a treatment for alcohol withdrawal alone.
If you've consumed large amounts of alcohol for a long time, withdrawal from alcohol can be life threatening, unlike withdrawal from opioids, which is extremely unpleasant but rarely life threatening.
Suboxone is an FDA approved medication for opioid withdrawal and can help ease cravings during acute opioid withdrawal .
If you are withdrawing from opioids as well as alcohol at the same time, it can be hard to distinguish which symptoms are from opioids and which might be from alcohol. Therefore, in such cases, taking Suboxone may help to make you feel better overall, but is still primarily treating the opioid withdrawal, not the alcohol withdrawal.
Alcohol withdrawal is a constellation of symptoms that occur when people who are dependent on alcohol stop drinking abruptly. Unlike with opioid withdrawal which is unpleasant but not life-threatening, alcohol withdrawal can range from very mild to severe and even life threatening. Thus, withdrawing from alcohol is actually more medically risky than withdrawing from opioids.
Symptoms of alcohol withdrawal start within about 4-8 hours of the last drink, and they usually peak at about 72 hours. They can last up to five days, after which point most patients are usually out of the window for any dangerous or life threatening complications of alcohol withdrawal. 
If you are withdrawing from alcohol, you might feel the following:
In serious cases, people begin to hallucinate, and they grow increasingly agitated. In time, you can develop life-threatening seizures, respiratory depression, or hypotension. These symptoms are most concerning and can even be life threatening. Anyone who has a history of seizures or hallucinations with alcohol cessation should ideally be monitored in the hospital while withdrawing from alcohol, and may even require intensive care.
The mainstay of treatment in the acute setting of alcohol withdrawal are usually benzodiazepine medications which calm your overactive nervous system and prevent seizures. Benzodiazepine medications boost GABA levels which is an inhibitory neurotransmitter in the brain.
Treatment teams typically administer benzodiazepines early in your alcohol detox program, and then taper you off of them slowly so that, at the end of your detox, your symptoms have resolved and you are no longer requiring benzodiazepines.
When you're done with detoxification, you have no alcohol in your body. But your cravings for a drink may remain. In these cases, you may benefit from a long term medication to help prevent relapse to alcohol use.
The U.S. Food and Drug Administration has approved four drugs for alcoholism treatment.
Suboxone alone is a treatment for opioid use disorder, not alcohol use disorder. Clinicians are not using Suboxone to treat AUD at this time.
Some people have looked into whether or not Suboxone also might reduce alcohol consumption:
One study with rats published in 2007 suggested that buprenorphine could be helpful in treating alcoholism  People aren't rats, and researchers must learn more about the connection between Suboxone and alcohol. But studies like this suggest that some people could benefit from taking Suboxone to curb their drinking. A secondary study in humans found positive results with Suboxone. People given the medication drank less, and some stopped drinking altogether.
It isn’t clear whether or not Suboxone is simply helping to reduce use of opioids which then also helps people to reduce substance use overall (including alcohol), or if Suboxone may actually act on cravings for alcohol directly.
In general, the best medications for alcohol use disorder at this time are Naltrexone, and possibly Acamprosate and Disulfiram as second line agents.
If you've tried to stop drinking and can't make the change stick, talk with your doctor about Medication for Addiction Treatment for alcoholism.