Bakkt shares more than tripled to $30.60. Mastercard shares rose 0.6% to $360.86.

Mastercard said in February that it was preparing to support cryptocurrencies on its network. The network said at the time that more people were using cards to buy crypto assets such as bitcoin and using crypto cards to access and convert these assets into traditional currencies for spending.

Mastercard is one of the largest card networks in the U.S., providing the infrastructure on which debit and credit card payments are processed. The company has been expanding its fintech partnerships and looking at ways to enable payments that go beyond traditional debit and credit cards.

One of the biggest risks for Mastercard and peer

Visa Inc.

is that a new form of payments that cuts out their networks could eventually develop and gain scale.

Major card networks and crypto fintech firms have announced other partnerships recently. In most of those deals, Visa or Mastercard serves as a network for a niche crypto card offered by the same fintech that houses the cardholders’ crypto assets. Bakkt, for example, currently offers its own Visa debit card.

Monday’s announcement has the potential to be more significant: Big banks would be able to offer crypto cards that are in part powered by Bakkt, potentially reaching a much larger number of consumers. Whether this broader offering takes off will in large part depend on banks’ appetite to issue these cards and consumers’ demand for them.

The cards would give consumers the ability to pay merchants with bitcoin.

Bakkt would convert that cryptocurrency into currency that the merchant accepts before sending the transaction over the Mastercard network. That will happen when the consumer makes the purchase. The company says the conversion would be done instantaneously so that the merchant isn’t affected by the volatility of cryptocurrencies.

Consumers’ cryptocurrencies would be stored in a wallet with Bakkt.

The partnership also would allow people to earn rewards in the form of cryptocurrencies rather than airline miles or other types of points. That offering could entice people who haven’t previously engaged with cryptocurrencies.

Write to AnnaMaria Andriotis at annamaria.andriotis@wsj.com