"Saudi Arabia has informed us that it saw its relationship with Sweden as normalised. As part of this, visas will be given again to Swedes. Exactly when, we cannot say," foreign ministry spokeswoman Catarina Axelsson told news Agency AFP.
The ministry also confirmed that the Saudi ambassador to Stockholm will return to Sweden this week.
The row between the two countries dates back to early March when Sweden's minister of foreign affairs, Margot Wallström, told parliament that Saudi Arabia was a "dictatorship" that violated human rights.
Sweden also announced that it would not be renewing a long-standing military cooperation deal between the two countries, which led the oil-rich state to prevent Margot Wallström from making a speech on human rights to the Arab League.
Saudi Arabia then recalled its ambassador to Stockholm on March 11 and froze Swedish business visas to the country.
Under pressure from the Swedish business community, upset over the potential loss of trade, Swedish politician Björn von Sydow travelled to Riyadh to deliver a letter to the Saudi monarch from Sweden's King Carl XVI and Prime Minister Stefan Löfven. Margot Wallström said that the letter apologised for what they termed as a misunderstanding.