Short Answer:

No. Most Medicare Advantage plans include integrated Medicare Part D prescription drug coverage (and are called MAPDs).  This drug coverage must comply with all of the same requirements as a stand-alone Medicare prescription drug plan.  However, some Medicare Advantage plans offer “medical services” only and DO NOT include the Part D prescription drug coverage (and are called MAs).

If you enroll in an “MA Only” plan, you are prohibited from purchasing a separate Part D plan unless the MA-Only plan is a Private fee-for-service or PFFS plan without drug coverage or an MSA plan. If you are enrolled in an Medicare Advantage HMO, enrolling in a Medicare Part D plan will automatically disenroll you from your HMO.

A few more details:

As noted, you cannot join an HMO Medicare Advantage plan that does not provide prescription coverage (MA HMO) and also enroll in a stand-alone Medicare Part D plan.  The MA HMO may work for people who are already receiving their prescription drug coverage from another source (such as VA drug coverage) - but they cannot be enrolled in a stand-alone Part D plan.  If you have a stand-alone Part D plan and try to join one of these MA HMO plans, you will lose your Part D coverage automatically.

The 2016 Medicare & You Handbook describes each type of Medicare Advantage plan and each has a section Are prescription drugs covered?  

• HMO plans - on page 90 it states "In most cases, yes.  If you want Medicare drug coverage, you must join an HMO plan that offers prescription drug coverage."
• PPO plans - on page 91 "In most cases, yes. If you want Medicare drug coverage, you must join a PPO plan that offers prescription drug coverage.
• PFFS plans - on page 92 - are a different story.  "Sometimes.  If you PFFS plan doesn't  offer drug coverage, you can join a Medicare Prescription Drug plan (Part D) to get coverage."  
• SNP - on page 93, "Yes. All SNPs must provide Medicare prescription drug coverage (Part D).

If you wish to find the Medicare Advantage plans in your area, you can use our MA-Finder:  MA-Finder.com. To see if a Medicare Advantage plan includes prescription drug coverage. Click here for an example of Medicare Advantage plans available in Allegheny County, Pennsylvania.

You can also browse for a Medicare Advantage plan by the counties in your state.   Here is an example of the Medicare Advantage plans for Florida counties: MA-Finder.com/FL or Texas using MA-Finder.com/TX, etc.

A bit of history:
The 2010 Medicare & You Handbook is a little confusing and on page 43 notes that for Medicare Advantage plans “like an HMO or PPO” you need, as the second step to “Decide If You Want Prescription Drug Coverage (Part D)” and "[i]f you want prescription drug coverage, and it’s offered by your plan, in most cases you must get it through your plan. If your plan doesn’t offer drug coverage, you can choose and join a Medicare Prescription Drug Plan. See pages 55–57." 

This statement is a little unclear.

However, on page 55, the subject of HMO and PPO Medicare Advantage plans are addressed and the handbook notes more directly that: “If you want drug coverage, you must join an HMO Plan that offers prescription drug coverage.”

The only thing that we can conclude is that the earlier page 43 of the 2010 Medicare & You handbook is referring to Medicare Advantage plans in the form of Private Fee for Service plans (PFFS) - that may allow you to join a separate stand-alone Medicare Part D plan along with the Medicare Advantage plan.

Here is a quote from an earlier Medicare & You Handbook that provides the information more clearly: 

"If you belong to a Medicare Advantage HMO or PPO, you can only get Medicare prescription drug coverage from your plan (if offered). If you join a stand-alone Medicare Prescription Drug Plan, you will be automatically disenrolled from your Medicare HMO or PPO and returned to the Original Medicare Plan."

As a note, in the early days of the Medicare Part D program, we had a few advocates that contacted us about how people joined these Medicare Advantage HMOs and immediately lost their Medicare Part D prescription drug coverage.

In short - if you wish to join a Medicare Advantage plan HMO, then you should look for a plan that also covers prescription drugs.

(Thanks to Gail S. for this question)