No, Destiny will be a free to play game.
While some MMO games like World of Warcraft charge a monthly fee, Bungie will not be doing that. And of course, Destiny is supposedly a FPS ‘persistent world’, rather than an MMO game so the business model is perhaps different.
Despite a well established desire quest for world domination, charging a subscription fee would be a sure fire way of turning fans off from purchasing the game.
Rather than chasing the subscription dollar, Bungie want their game everywhere to get the increased sales window. By being on the the Playstation, on the Xbox, on your smart phone, being on the PC – that increases the opportunity for gamers to consider buying the game.
Bungie and Activision (the game publisher) will also no doubt invest heavily in producing DLC for in game missions, maps and possibly even microtransactions (just guess there) – there’s good money to be made in DLC so surely they’ll look to this revenue stream.
Finally, one factor that Bungie will be absolutely counting on is that their 'Halo fans' will check out the game. Those fans come from the Xbox realm and are just not used to doing subscription based gaming so would probably not be interested if that was the case.
The Halo / Bungie fan community are probably the group that will make or break this game – their support in getting the word out about Destiny will be a crucial factor in any success. So, no way will Bungie want to alienate that group by charging them a monthly subscription.