Neymar suffered a fractured vertebra following a challenge with Juan Camilo Zuniga in Brazil's World Cup quarter-final clash with Colombia and was not involved in Barca's 1-1 friendly draw with Nice.
However, Alba believes the forward will quickly be back to full fitness, telling reporters: "Neymar is very eager and excited, he'll recover quickly. He's very happy at Barcelona and, for us, he's an important player."
New boss Luis Enrique's proposed tactical switch to 3-2-3-2 has led to some concerns over Alba's place in the starting line-up for the new season but the Spain full-back says the coach's ideas are perfectly suited to the club.
"The ideas of Luis Enrique are very good for our style of football, the team is already mentally set to adopt them. This friendly will help us move one step further in our bid to begin La Liga in the best possible form," he said.
"Luis Enrique and his coaching staff can do great things. He's the right person at this time."
Barca face Napoli in a pre-season friendly on Wednesday.