If we opt Azure SQL managed instances in DEV,QA and PROD environment . Will Microsoft take care the DB maintenance in terms of index rebuild or reorganize periodically etc. ?
Azure does not automatically rebuild your indexes. You need to maintain the SQL indexes.
There is a blog article on how you can automate these tasks here: https://geeks.ms/davidjrh/2015/10/08/rebuilding-sql-database-indexes-using-azure-automation/